/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files


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Graph construction failed
Graph construction failed
Graph construction failed
MAYBE
proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

play(g,g,a)

w.r.t. the given Prolog program could not be shown:

(0) Prolog
(1) NotTransformerProof [EQUIVALENT, 0 ms]
(2) Prolog
    (3) CallTransformerProof [EQUIVALENT, 0 ms]
    (4) Prolog
    (5) CutEliminatorProof [SOUND, 0 ms]
    (6) Prolog
    (7) FailTransformerProof [EQUIVALENT, 0 ms]
    (8) Prolog
    (9) UnifyTransformerProof [EQUIVALENT, 0 ms]
    (10) Prolog
    (11) UndefinedPredicateHandlerProof [SOUND, 0 ms]
    (12) Prolog
(13) IntegerArithmeticTransformerProof [SOUND, 0 ms]
(14) Prolog
    (15) NotTransformerProof [EQUIVALENT, 0 ms]
    (16) Prolog
    (17) CallTransformerProof [EQUIVALENT, 0 ms]
    (18) Prolog
    (19) CutEliminatorProof [SOUND, 0 ms]
    (20) Prolog
    (21) FailTransformerProof [EQUIVALENT, 0 ms]
    (22) Prolog
    (23) UnifyTransformerProof [EQUIVALENT, 0 ms]
    (24) Prolog
    (25) OrTransformerProof [EQUIVALENT, 0 ms]
    (26) Prolog
    (27) UndefinedPredicateHandlerProof [SOUND, 0 ms]
    (28) Prolog


----------------------------------------

(0)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(!, ','(write(Result), abolish0(player)))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), ','(!, play(Position1, Player1, Result)))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, -1, 1, Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), is(Value, 0)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(is(Alpha1, -(Beta)), ','(is(Beta1, -(Alpha)), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(is(Value1, -(Value)), ','(cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best), !))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(>=(Value, Beta), !).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(<(Alpha, Value), ','(<(Value, Beta), ','(!, evaluate(Player, Moves, Position, Value, Beta, Move, Best)))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=<(Value, Alpha), ','(!, evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(3), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(3), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(3), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), ','(!, choose(Position, Player, Move))).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(\+(game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))), ','(\+(game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(1) NotTransformerProof (EQUIVALENT)
Transformed all not-constructs [PROLOG].
----------------------------------------

(2)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(!, ','(write(Result), abolish0(player)))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), ','(!, play(Position1, Player1, Result)))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, -1, 1, Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), is(Value, 0)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(is(Alpha1, -(Beta)), ','(is(Beta1, -(Alpha)), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(is(Value1, -(Value)), ','(cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best), !))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(>=(Value, Beta), !).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(<(Alpha, Value), ','(<(Value, Beta), ','(!, evaluate(Player, Moves, Position, Value, Beta, Move, Best)))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=<(Value, Alpha), ','(!, evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(3), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(3), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(3), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), ','(!, choose(Position, Player, Move))).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call(game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))), ','(!, fail)).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call(game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))), ','(!, fail)).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(3) CallTransformerProof (EQUIVALENT)
Transformed all call-constructs [PROLOG].
----------------------------------------

(4)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(!, ','(write(Result), abolish0(player)))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), ','(!, play(Position1, Player1, Result)))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, -1, 1, Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), is(Value, 0)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(is(Alpha1, -(Beta)), ','(is(Beta1, -(Alpha)), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(is(Value1, -(Value)), ','(cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best), !))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(>=(Value, Beta), !).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(<(Alpha, Value), ','(<(Value, Beta), ','(!, evaluate(Player, Moves, Position, Value, Beta, Move, Best)))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=<(Value, Alpha), ','(!, evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(3), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(3), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(3), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), ','(!, choose(Position, Player, Move))).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(!, fail)).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(!, fail)).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(5) CutEliminatorProof (SOUND)
Eliminated all cuts by simply ignoring them[PROLOG].
----------------------------------------

(6)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, -1, 1, Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), is(Value, 0)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(is(Alpha1, -(Beta)), ','(is(Beta1, -(Alpha)), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(is(Value1, -(Value)), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- >=(Value, Beta).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(<(Alpha, Value), ','(<(Value, Beta), evaluate(Player, Moves, Position, Value, Beta, Move, Best))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=<(Value, Alpha), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(3), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(3), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(3), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(7) FailTransformerProof (EQUIVALENT)
Added clauses for the built-in fail predicate [PROLOG].
----------------------------------------

(8)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, -1, 1, Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), is(Value, 0)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(is(Alpha1, -(Beta)), ','(is(Beta1, -(Alpha)), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(is(Value1, -(Value)), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- >=(Value, Beta).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(<(Alpha, Value), ','(<(Value, Beta), evaluate(Player, Moves, Position, Value, Beta, Move, Best))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=<(Value, Alpha), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(3), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(3), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(3), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
fail :- failure(a).
failure(b).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(9) UnifyTransformerProof (EQUIVALENT)
Added a fact for the built-in = predicate [PROLOG].
----------------------------------------

(10)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, -1, 1, Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), is(Value, 0)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(is(Alpha1, -(Beta)), ','(is(Beta1, -(Alpha)), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(is(Value1, -(Value)), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- >=(Value, Beta).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(<(Alpha, Value), ','(<(Value, Beta), evaluate(Player, Moves, Position, Value, Beta, Move, Best))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=<(Value, Alpha), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(3), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(3), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(3), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
fail :- failure(a).
failure(b).
=(X, X).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(11) UndefinedPredicateHandlerProof (SOUND)
Added facts for all undefined predicates [PROLOG].
----------------------------------------

(12)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, -1, 1, Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), is(Value, 1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), is(Value, 0)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), is(Value, -1))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(is(Alpha1, -(Beta)), ','(is(Beta1, -(Alpha)), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(is(Value1, -(Value)), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- >=(Value, Beta).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(<(Alpha, Value), ','(<(Value, Beta), evaluate(Player, Moves, Position, Value, Beta, Move, Best))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=<(Value, Alpha), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(3), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(3), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(3), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
fail :- failure(a).
failure(b).
=(X, X).
write(X0).
abolish0(X0).
nl.
read(X0).
==(X0, X1).
is(X0, X1).
player(X0).
setof(X0, X1, X2).
>=(X0, X1).
<(X0, X1).
=<(X0, X1).
assert(X0).
tab(X0).
\==(X0, X1).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(13) IntegerArithmeticTransformerProof (SOUND)
Added definitions of predefined predicates [PROLOG].
----------------------------------------

(14)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(!, ','(write(Result), abolish0(player)))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), ','(!, play(Position1, Player1, Result)))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, pred(zero), succ(zero), Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), =(Value, zero)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(isMinus(zero1, Beta, U), ','(=(Alpha1, U), ','(isMinus(zero1, Alpha, U), ','(=(Beta1, U), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(isMinus(zero1, Value, U), ','(=(Value1, U), ','(cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best), !)))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), ','(;(isGreater(X, X1), =(X, X1)), !))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Alpha), ','(=(X1, Value), ','(isLess(X, X1), ','(=(X2, Value), ','(=(X3, Beta), ','(isLess(X2, X3), ','(!, evaluate(Player, Moves, Position, Value, Beta, Move, Best)))))))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(;(=(X, X1), isLess(X, X1)), ','(!, evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best))))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), ','(!, choose(Position, Player, Move))).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(\+(game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))), ','(\+(game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(15) NotTransformerProof (EQUIVALENT)
Transformed all not-constructs [PROLOG].
----------------------------------------

(16)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(!, ','(write(Result), abolish0(player)))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), ','(!, play(Position1, Player1, Result)))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, pred(zero), succ(zero), Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), =(Value, zero)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(isMinus(zero1, Beta, U), ','(=(Alpha1, U), ','(isMinus(zero1, Alpha, U), ','(=(Beta1, U), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(isMinus(zero1, Value, U), ','(=(Value1, U), ','(cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best), !)))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), ','(;(isGreater(X, X1), =(X, X1)), !))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Alpha), ','(=(X1, Value), ','(isLess(X, X1), ','(=(X2, Value), ','(=(X3, Beta), ','(isLess(X2, X3), ','(!, evaluate(Player, Moves, Position, Value, Beta, Move, Best)))))))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(;(=(X, X1), isLess(X, X1)), ','(!, evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best))))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), ','(!, choose(Position, Player, Move))).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call(game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))), ','(!, fail)).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call(game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))), ','(!, fail)).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(17) CallTransformerProof (EQUIVALENT)
Transformed all call-constructs [PROLOG].
----------------------------------------

(18)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(!, ','(write(Result), abolish0(player)))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), ','(!, play(Position1, Player1, Result)))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, pred(zero), succ(zero), Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), =(Value, zero)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(isMinus(zero1, Beta, U), ','(=(Alpha1, U), ','(isMinus(zero1, Alpha, U), ','(=(Beta1, U), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(isMinus(zero1, Value, U), ','(=(Value1, U), ','(cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best), !)))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), ','(;(isGreater(X, X1), =(X, X1)), !))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Alpha), ','(=(X1, Value), ','(isLess(X, X1), ','(=(X2, Value), ','(=(X3, Beta), ','(isLess(X2, X3), ','(!, evaluate(Player, Moves, Position, Value, Beta, Move, Best)))))))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(;(=(X, X1), isLess(X, X1)), ','(!, evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best))))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), ','(!, choose(Position, Player, Move))).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(!, fail)).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(!, fail)).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(19) CutEliminatorProof (SOUND)
Eliminated all cuts by simply ignoring them[PROLOG].
----------------------------------------

(20)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, pred(zero), succ(zero), Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), =(Value, zero)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(isMinus(zero1, Beta, U), ','(=(Alpha1, U), ','(isMinus(zero1, Alpha, U), ','(=(Beta1, U), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(isMinus(zero1, Value, U), ','(=(Value1, U), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best)))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), ;(isGreater(X, X1), =(X, X1)))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Alpha), ','(=(X1, Value), ','(isLess(X, X1), ','(=(X2, Value), ','(=(X3, Beta), ','(isLess(X2, X3), evaluate(Player, Moves, Position, Value, Beta, Move, Best))))))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(;(=(X, X1), isLess(X, X1)), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(21) FailTransformerProof (EQUIVALENT)
Added clauses for the built-in fail predicate [PROLOG].
----------------------------------------

(22)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, pred(zero), succ(zero), Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), =(Value, zero)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(isMinus(zero1, Beta, U), ','(=(Alpha1, U), ','(isMinus(zero1, Alpha, U), ','(=(Beta1, U), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(isMinus(zero1, Value, U), ','(=(Value1, U), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best)))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), ;(isGreater(X, X1), =(X, X1)))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Alpha), ','(=(X1, Value), ','(isLess(X, X1), ','(=(X2, Value), ','(=(X3, Beta), ','(isLess(X2, X3), evaluate(Player, Moves, Position, Value, Beta, Move, Best))))))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(;(=(X, X1), isLess(X, X1)), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
fail :- failure(a).
failure(b).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(23) UnifyTransformerProof (EQUIVALENT)
Added a fact for the built-in = predicate [PROLOG].
----------------------------------------

(24)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, pred(zero), succ(zero), Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), =(Value, zero)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(isMinus(zero1, Beta, U), ','(=(Alpha1, U), ','(isMinus(zero1, Alpha, U), ','(=(Beta1, U), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(isMinus(zero1, Value, U), ','(=(Value1, U), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best)))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), ;(isGreater(X, X1), =(X, X1)))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Alpha), ','(=(X1, Value), ','(isLess(X, X1), ','(=(X2, Value), ','(=(X3, Beta), ','(isLess(X2, X3), evaluate(Player, Moves, Position, Value, Beta, Move, Best))))))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(;(=(X, X1), isLess(X, X1)), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
fail :- failure(a).
failure(b).
=(X, X).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(25) OrTransformerProof (EQUIVALENT)
Transformed all or-constructs[PROLOG].
----------------------------------------

(26)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, pred(zero), succ(zero), Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), =(Value, zero)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(isMinus(zero1, Beta, U), ','(=(Alpha1, U), ','(isMinus(zero1, Alpha, U), ','(=(Beta1, U), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(isMinus(zero1, Value, U), ','(=(Value1, U), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best)))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), isGreater(X, X1))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), =(X, X1))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Alpha), ','(=(X1, Value), ','(isLess(X, X1), ','(=(X2, Value), ','(=(X3, Beta), ','(isLess(X2, X3), evaluate(Player, Moves, Position, Value, Beta, Move, Best))))))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(=(X, X1), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(isLess(X, X1), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
fail :- failure(a).
failure(b).
=(X, X).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)
----------------------------------------

(27) UndefinedPredicateHandlerProof (SOUND)
Added facts for all undefined predicates [PROLOG].
----------------------------------------

(28)
Obligation:
Clauses:

play(Game) :- ','(initialize(Game, Position, Player), ','(display_game(Position), play(Position, Player, Result))).
play(Position, Player, Result) :- ','(game_over(Position, Player, Result), ','(write(Result), abolish0(player))).
play(Position, Player, Result) :- ','(choose(Position, Player, Move), ','(move(Move, Player, Position, Position1), ','(display_game(Position1), ','(next_player(Player, Player1), play(Position1, Player1, Result))))).
choose(Position, computer, Move) :- ','(write('Computer is thinking...'), ','(nl, alpha_beta(computer, Position, pred(zero), succ(zero), Move, Value))).
choose(Position, Player, Move) :- ','(write(Player), ','(write(', enter move (followed by a period and return) --> '), ','(read(Move1), legal(Position, Player, Move1, Move)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_o(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_x(Position), =(Value, succ(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(game_tie(Position), =(Value, zero)).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(==(Player, computer), ','(game_win_x(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(player(Player), ','(game_win_o(Position), =(Value, pred(zero)))).
alpha_beta(Player, Position, Alpha, Beta, Move, Value) :- ','(setof(Move1, move(Position, Move1), Moves), ','(isMinus(zero1, Beta, U), ','(=(Alpha1, U), ','(isMinus(zero1, Alpha, U), ','(=(Beta1, U), evaluate(Player, Moves, Position, Alpha1, Beta1, nil, ','(Move, Value))))))).
evaluate(Player, .(Move, Moves), Position, Alpha, Beta, Move1, Best) :- ','(move(Move, Player, Position, Position1), ','(next_player(Player, Player1), ','(alpha_beta(Player1, Position1, Alpha, Beta, MoveX, Value), ','(isMinus(zero1, Value, U), ','(=(Value1, U), cutoff(Player, Move, Value1, Alpha, Beta, Moves, Position, Move1, Best)))))).
evaluate(Player, [], Position, Alpha, Beta, Move, ','(Move, Alpha)).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), isGreater(X, X1))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, ','(Move, Value)) :- ','(=(X, Value), ','(=(X1, Beta), =(X, X1))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Alpha), ','(=(X1, Value), ','(isLess(X, X1), ','(=(X2, Value), ','(=(X3, Beta), ','(isLess(X2, X3), evaluate(Player, Moves, Position, Value, Beta, Move, Best))))))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(=(X, X1), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)))).
cutoff(Player, Move, Value, Alpha, Beta, Moves, Position, Move1, Best) :- ','(=(X, Value), ','(=(X1, Alpha), ','(isLess(X, X1), evaluate(Player, Moves, Position, Alpha, Beta, Move1, Best)))).
initialize(tictactoe, ','(','(' ', ','(' ', ' ')), ','(','(' ', ','(' ', ' ')), ','(' ', ','(' ', ' ')))), Player) :- ','(write('Enter player`s name (followed by a period and return) --> '), ','(read(Player), ','(write(Player), ','(write(', you will go first and use the symbol "x".'), ','(nl, assert(player(Player))))))).
display_game(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(nl, ','(write(' '), ','(write(R1C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R1C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('u-l = upper left,  u-c = upper center,  u-r = upper right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R2C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R2C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('c-l = center left, c-c = center center, c-r = center right'), ','(nl, ','(write(' --+---+-- '), ','(nl, ','(write(' '), ','(write(R3C1), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C2), ','(write(' '), ','(write('|'), ','(write(' '), ','(write(R3C3), ','(write(' '), ','(tab(succ(succ(succ(zero)))), ','(write('l-l = lower left,  l-c = lower center,  l-r = lower right'), ','(nl, nl))))))))))))))))))))))))))))))))))))))))))))))).
next_player(Player, computer) :- player(Player).
next_player(computer, Player1) :- player(Player1).
legal(Position, Player, Move, Move) :- move(Position, Move).
legal(Position, Player, Move1, Move) :- ','(write('Illegal move!  '), choose(Position, Player, Move)).
game_over(Position, Player, ','(Player1, ' you win!')) :- ','(game_win_x(Position), player(Player1)).
game_over(Position, Player, 'Computer wins!') :- game_win_o(Position).
game_over(Position, Player, 'It is a tie!') :- game_tie(Position).
game_tie(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))) :- ','(not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), ','(\==(R1C1, ' '), ','(\==(R1C2, ' '), ','(\==(R1C3, ' '), ','(\==(R2C1, ' '), ','(\==(R2C2, ' '), ','(\==(R2C3, ' '), ','(\==(R3C1, ' '), ','(\==(R3C2, ' '), \==(R3C3, ' '))))))))))).
game_win_x(','(','(x, ','(x, x)), ','(','(X1, ','(X2, X3)), ','(X4, ','(X5, X6))))).
game_win_x(','(','(X7, ','(X8, X9)), ','(','(x, ','(x, x)), ','(X10, ','(X11, X12))))).
game_win_x(','(','(X13, ','(X14, X15)), ','(','(X16, ','(X17, X18)), ','(x, ','(x, x))))).
game_win_x(','(','(x, ','(X19, X20)), ','(','(x, ','(X21, X22)), ','(x, ','(X23, X24))))).
game_win_x(','(','(X25, ','(x, X26)), ','(','(X27, ','(x, X28)), ','(X29, ','(x, X30))))).
game_win_x(','(','(X31, ','(X32, x)), ','(','(X33, ','(X34, x)), ','(X35, ','(X36, x))))).
game_win_x(','(','(x, ','(X37, X38)), ','(','(X39, ','(x, X40)), ','(X41, ','(X42, x))))).
game_win_x(','(','(X43, ','(X44, x)), ','(','(X45, ','(x, X46)), ','(x, ','(X47, X48))))).
game_win_o(','(','(o, ','(o, o)), ','(','(X49, ','(X50, X51)), ','(X52, ','(X53, X54))))).
game_win_o(','(','(X55, ','(X56, X57)), ','(','(o, ','(o, o)), ','(X58, ','(X59, X60))))).
game_win_o(','(','(X61, ','(X62, X63)), ','(','(X64, ','(X65, X66)), ','(o, ','(o, o))))).
game_win_o(','(','(o, ','(X67, X68)), ','(','(o, ','(X69, X70)), ','(o, ','(X71, X72))))).
game_win_o(','(','(X73, ','(o, X74)), ','(','(X75, ','(o, X76)), ','(X77, ','(o, X78))))).
game_win_o(','(','(X79, ','(X80, o)), ','(','(X81, ','(X82, o)), ','(X83, ','(X84, o))))).
game_win_o(','(','(o, ','(X85, X86)), ','(','(X87, ','(o, X88)), ','(X89, ','(X90, o))))).
game_win_o(','(','(X91, ','(X92, o)), ','(','(X93, ','(o, X94)), ','(o, ','(X95, X96))))).
move(','(','(' ', ','(X97, X98)), ','(','(X99, ','(X100, X101)), ','(X102, ','(X103, X104)))), -(u, l)).
move(','(','(X105, ','(' ', X106)), ','(','(X107, ','(X108, X109)), ','(X110, ','(X111, X112)))), -(u, c)).
move(','(','(X113, ','(X114, ' ')), ','(','(X115, ','(X116, X117)), ','(X118, ','(X119, X120)))), -(u, r)).
move(','(','(X121, ','(X122, X123)), ','(','(' ', ','(X124, X125)), ','(X126, ','(X127, X128)))), -(c, l)).
move(','(','(X129, ','(X130, X131)), ','(','(X132, ','(' ', X133)), ','(X134, ','(X135, X136)))), -(c, c)).
move(','(','(X137, ','(X138, X139)), ','(','(X140, ','(X141, ' ')), ','(X142, ','(X143, X144)))), -(c, r)).
move(','(','(X145, ','(X146, X147)), ','(','(X148, ','(X149, X150)), ','(' ', ','(X151, X152)))), -(l, l)).
move(','(','(X153, ','(X154, X155)), ','(','(X156, ','(X157, X158)), ','(X159, ','(' ', X160)))), -(l, c)).
move(','(','(X161, ','(X162, X163)), ','(','(X164, ','(X165, X166)), ','(X167, ','(X168, ' ')))), -(l, r)).
move(-(u, l), computer, Position, Position1) :- ','(=(','(','(X169, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(o, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(X170, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(o, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X171)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, o)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X172, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(o, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X173, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(o, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X174)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, o)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X175, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(o, ','(R3C2, R3C3)))))).
move(-(l, c), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X176, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(o, R3C3)))))).
move(-(l, r), computer, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X177)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, o)))))).
move(-(u, l), Player, Position, Position1) :- ','(=(','(','(X178, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(x, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(X179, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(x, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(u, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, X180)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, x)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(X181, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(x, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(X182, R2C3)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(x, R2C3)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(c, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, X183)), ','(R3C1, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, x)), ','(R3C1, ','(R3C2, R3C3)))))).
move(-(l, l), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(X184, ','(R3C2, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(x, ','(R3C2, R3C3)))))).
move(-(l, c), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(X185, R3C3)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(x, R3C3)))))).
move(-(l, r), Player, Position, Position1) :- ','(=(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, X186)))), Position), =(Position1, ','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, x)))))).
isPlus(zero, X, X).
isPlus(succ(X), zero, succ(X)).
isPlus(succ(X), succ(Y), succ(succ(Z))) :- isPlus(X, Y, Z).
isPlus(succ(X), pred(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), zero, pred(X)).
isPlus(pred(X), succ(Y), Z) :- isPlus(X, Y, Z).
isPlus(pred(X), pred(Y), pred(pred(Z))) :- isPlus(X, Y, Z).
isMinus(X, zero, X).
isMinus(zero, succ(Y), pred(Z)) :- isMinus(zero, Y, Z).
isMinus(zero, pred(Y), succ(Z)) :- isMinus(zero, Y, Z).
isMinus(succ(X), succ(Y), Z) :- isMinus(X, Y, Z).
isMinus(succ(X), pred(Y), succ(succ(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), succ(Y), pred(pred(Z))) :- isMinus(X, Y, Z).
isMinus(pred(X), pred(Y), Z) :- isMinus(X, Y, Z).
isTimes(X, zero, zero).
isTimes(zero, succ(Y), zero).
isTimes(zero, pred(Y), zero).
isTimes(succ(X), succ(Y), Z) :- ','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).
isTimes(succ(X), pred(Y), Z) :- ','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).
isTimes(pred(X), succ(Y), Z) :- ','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).
isTimes(pred(X), pred(Y), Z) :- ','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).
isDiv(zero, succ(Y), zero).
isDiv(zero, pred(Y), zero).
isDiv(succ(X), succ(Y), zero) :- isMinus(succ(X), succ(Y), pred(Z)).
isDiv(succ(X), succ(Y), succ(Z)) :- ','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).
isDiv(succ(X), pred(Y), Z) :- ','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).
isDiv(pred(X), pred(Y), zero) :- isMinus(pred(X), pred(Y), succ(Z)).
isDiv(pred(X), pred(Y), succ(Z)) :- ','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).
isDiv(pred(X), succ(Y), Z) :- ','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).
isModulo(X, Y, Z) :- ','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).
isGreater(succ(X), zero).
isGreater(succ(X), pred(Y)).
isGreater(succ(X), succ(Y)) :- isGreater(X, Y).
isGreater(zero, pred(Y)).
isGreater(pred(X), pred(Y)) :- isGreater(X, Y).
isLess(pred(X), zero).
isLess(pred(X), succ(Y)).
isLess(pred(X), pred(Y)) :- isLess(X, Y).
isLess(zero, succ(Y)).
isLess(succ(X), succ(Y)) :- isLess(X, Y).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- ','(call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3), fail).
not1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3).
call1(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_x(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
call2(R1C1, R1C2, R1C3, R2C1, R2C2, R2C3, R3C1, R3C2, R3C3) :- game_win_o(','(','(R1C1, ','(R1C2, R1C3)), ','(','(R2C1, ','(R2C2, R2C3)), ','(R3C1, ','(R3C2, R3C3))))).
fail :- failure(a).
failure(b).
=(X, X).
write(X0).
abolish0(X0).
nl.
read(X0).
==(X0, X1).
player(X0).
setof(X0, X1, X2).
assert(X0).
tab(X0).
\==(X0, X1).

Directives:

:- entry(play(Game), .(ground(Game), [])).
:- trust(player(Player), [], .(ground(Player), [])).
:- trust(abolish0(Player), [], .(ground(Player), [])).


Query: play(g,g,a)