TPTP Axioms File: PLA002+0.ax
%--------------------------------------------------------------------------
% File : PLA002+0 : TPTP v8.2.0. Released v2.4.0.
% Domain : Planning (Blocks world)
% Axioms : Blocks world axioms
% Version : [Bau99] axioms.
% English :
% Refs : [Bau99] Baumgartner (1999), FTP'2000 - Problem Sets
% [KS96] Kautz & Selman (1996), Pushing the Envelope: Planning,
% [KS92] Kautz & Selman (1992), Planning as Satisfiability
% Source : [Bau99]
% Names :
% Status : Satisfiable
% Syntax : Number of formulae : 24 ( 0 unt; 0 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 120 ( 25 ~; 0 |; 43 &)
% ( 0 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 10 usr; 0 prp; 1-3 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% SPC :
% Comments :
%--------------------------------------------------------------------------
% blocks_axioms:
fof(place_object_block_on_destination,axiom,
! [I,X] :
( nonfixed(X)
=> ! [Z] :
( ( a_block(Z)
& neq(X,Z) )
=> ( ( time(I)
& object(X,I)
& destination(Z,I) )
=> on(X,Z,s(I)) ) ) ) ).
% All( x, block, ! member( x, fixed),
% All( y, block, ! eql( x, y),
% Disj(
% Not( L2("object", x, i));
% Not( L2("source", y, i));
% Not( L3("on", x, y, 1 + i)))));
fof(remove_object_block_from_source,axiom,
! [I,X] :
( nonfixed(X)
=> ! [Y] :
( ( a_block(Y)
& neq(X,Y) )
=> ( ( time(I)
& object(X,I)
& source(Y,I) )
=> ~ on(X,Y,s(I)) ) ) ) ).
% All( y, block, ! member( y, fixed),
% Disj(
% Not( L2("source", y, i));
% L2("clear", y, 1 + i);
% ));
fof(clear_source_after_removal,axiom,
! [I,Y] :
( nonfixed(Y)
=> ( ( time(I)
& source(Y,I) )
=> clear(Y,s(I)) ) ) ).
% All( z, block, ! member( z, fixed),
% Disj(
% Not( L2("destination", z, i));
% Not( L2("clear", z, 1 + i))));
fof(not_clear_destination_after_placement,axiom,
! [I,Z] :
( nonfixed(Z)
=> ( ( time(I)
& destination(Z,I) )
=> ~ clear(Z,s(I)) ) ) ).
fof(object_block_on_source,axiom,
! [I,X] :
( nonfixed(X)
=> ! [Y] :
( ( a_block(Y)
& neq(X,Y) )
=> ( ( object(X,I)
& source(Y,I) )
=> on(X,Y,I) ) ) ) ).
% All( x, block, ! member( x, fixed),
% Disj(
% Not( L2("object", x, i));
% L2("clear", x, i)));
fof(object_block_is_clear,axiom,
! [I,X] :
( nonfixed(X)
=> ( object(X,I)
=> clear(X,I) ) ) ).
% All( z, block, ! member( z, fixed),
% Disj(
% Not( L2("destination", z, i));
% L2("clear", z, i)));
fof(destination_block_is_clear,axiom,
! [I,Z] :
( nonfixed(Z)
=> ( destination(Z,I)
=> clear(Z,I) ) ) ).
fof(non_destination_remains_clear,axiom,
! [I,W] :
( nonfixed(W)
=> ( ( time(I)
& ~ destination(W,I)
& clear(W,I) )
=> clear(W,s(I)) ) ) ).
% All( v, block, ! member( v, fixed),
% All( w, block, !eql( v, w),
% Disj(
% L2("object", v, i);
% Not( L3("on", v, w, i)) ;
% L3("on", v, w, 1 + i))));
fof(non_object_remains_on,axiom,
! [I,V] :
( nonfixed(V)
=> ! [W] :
( ( a_block(W)
& neq(V,W) )
=> ( ( time(I)
& ~ object(V,I)
& on(V,W,I) )
=> on(V,W,s(I)) ) ) ) ).
fof(non_source_remains_not_clear,axiom,
! [I,W] :
( nonfixed(W)
=> ( ( time(I)
& ~ source(W,I)
& ~ clear(W,I) )
=> ~ clear(W,s(I)) ) ) ).
% All( v, block, ! member( v, fixed),
% All( w, block, ! eql( v, w),
% Disj(
% L2("object", v, i);
% L3("on", v, w, i) ;
% Not( L3("on", v, w, 1 + i)))));
fof(non_object_remains_not_on,axiom,
! [I,V] :
( nonfixed(V)
=> ! [W] :
( ( a_block(W)
& neq(V,W) )
=> ( ( time(I)
& ~ object(V,I)
& ~ on(V,W,I) )
=> ~ on(V,W,s(I)) ) ) ) ).
% All( v, block, ! member( v, fixed),
% All( w, block, ! eql( v, w),
% Disj(
% L2("destination", w, i);
% L3("on", v, w, i);
% Not( L3("on", v, w, 1 + i)))));
fof(non_destination_remains_not_on,axiom,
! [I,V] :
( nonfixed(V)
=> ! [W] :
( ( a_block(W)
& neq(V,W) )
=> ( ( time(I)
& ~ destination(W,I)
& ~ on(V,W,I) )
=> ~ on(V,W,s(I)) ) ) ) ).
fof(only_one_object_block,axiom,
! [I,X1] :
( nonfixed(X1)
=> ! [X2] :
( ( a_block(X2)
& neq(X1,X2) )
=> ~ ( object(X1,I)
& object(X2,I) ) ) ) ).
% All( y1, block, 1,
% All( y2, block, ! eql( y1, y2),
% Disj(
% Not( L2("source", y1, i));
% Not( L2("source", y2, i)))));
fof(only_one_source_block,axiom,
! [I,Y1] :
( a_block(Y1)
=> ! [Y2] :
( ( a_block(Y2)
& neq(Y1,Y2) )
=> ~ ( source(Y1,I)
& source(Y2,I) ) ) ) ).
% All( z1, block, 1,
% All( z2, block, ! eql( z1, z2),
% Disj(
% Not( L2("destination", z1, i));
% Not( L2("destination", z2, i)))));
fof(only_one_destination_block,axiom,
! [I,Z1] :
( a_block(Z1)
=> ! [Z2] :
( ( a_block(Z2)
& neq(Z1,Z2) )
=> ~ ( destination(Z1,I)
& destination(Z2,I) ) ) ) ).
fof(object_is_not_source,axiom,
! [I,X] :
( nonfixed(X)
=> ~ ( object(X,I)
& source(X,I) ) ) ).
% All( x, block, ! member( x, fixed),
% Disj(
% Not( L2("object", x, i));
% Not( L2("destination", x, i))));
fof(object_is_not_destination,axiom,
! [I,X] :
( nonfixed(X)
=> ~ ( object(X,I)
& destination(X,I) ) ) ).
% All( y, block, y,
% Disj(
% Not( L2("source", y, i));
% Not( L2("destination", y, i))));
fof(source_is_not_destination,axiom,
! [I,Y] :
( a_block(Y)
=> ~ ( source(Y,I)
& destination(Y,I) ) ) ).
%% on_axioms:
fof(not_on_each_other,axiom,
! [I,X] :
( a_block(X)
=> ! [Y] :
( ( a_block(Y)
& neq(X,Y) )
=> ~ ( on(X,Y,I)
& on(Y,X,I) ) ) ) ).
fof(not_on_self,axiom,
! [I,X] :
( a_block(X)
=> ~ on(X,X,I) ) ).
fof(only_one_on,axiom,
! [I,X] :
( nonfixed(X)
=> ! [Y] :
( ( nonfixed(Y)
& neq(X,Y) )
=> ! [Z] :
( ( nonfixed(Z)
& neq(X,Z)
& neq(Y,Z) )
=> ~ ( on(X,Y,I)
& on(Z,Y,I) ) ) ) ) ).
fof(only_on_one_thing,axiom,
! [I,X] :
( nonfixed(X)
=> ! [Y] :
( ( a_block(Y)
& neq(X,Y) )
=> ! [Z] :
( ( a_block(Z)
& neq(X,Z)
& neq(Y,Z) )
=> ~ ( on(X,Y,I)
& on(X,Z,I) ) ) ) ) ).
fof(not_clear_if_something_on,axiom,
! [I,X] :
( nonfixed(X)
=> ! [Y] :
( nonfixed(Y)
=> ~ ( on(X,Y,I)
& clear(Y,I) ) ) ) ).
fof(fixed_not_on_anything,axiom,
! [I,X] :
( a_block(X)
=> ! [Y] :
( fixed(Y)
=> ~ on(Y,X,I) ) ) ).
%--------------------------------------------------------------------------