%------------------------------------------------------------------------------
% File : LCL946_10 : TPTP v8.2.0. Released v8.2.0.
% Domain : Natural Language Processing
% Problem : Goedel translation of NLP009+1
% Version : [QMLTP] axioms.
% English :
% Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source : [QMLTP]
% Names : GNL009+1 [QMLTP]
% Status : Unknown
% Rating : 1.00 v8.2.0
% Syntax : Number of formulae : 55 ( 2 unt; 25 typ; 0 def)
% Number of atoms : 562 ( 0 equ)
% Maximal formula atoms : 266 ( 18 avg)
% Number of connectives : 536 ( 4 ~; 0 |; 170 &)
% ( 0 <=>; 362 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 16 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 50 ( 23 >; 27 *; 0 +; 0 <<)
% Number of predicates : 23 ( 23 usr; 0 prp; 2-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 376 (; 339 !; 37 ?; 376 :)
% SPC : TF0_UNK_NEQ_NAR
% Comments : Generated by embedproblem, version 1.7.14, rigid constant,
% modal_system_S4, TFF embedding.
%------------------------------------------------------------------------------
tff('$ki_world_type',type,
'$ki_world': $tType ).
tff('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
tff('$ki_accessible_decl',type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(mrel_reflexive,axiom,
! [W: '$ki_world'] : '$ki_accessible'(W,W) ).
tff(mrel_transitive,axiom,
! [W: '$ki_world',V: '$ki_world',U: '$ki_world'] :
( ( '$ki_accessible'(W,V)
& '$ki_accessible'(V,U) )
=> '$ki_accessible'(W,U) ) ).
tff(chevy_decl,type,
chevy: ( '$ki_world' * $i ) > $o ).
tff(dirty_decl,type,
dirty: ( '$ki_world' * $i ) > $o ).
tff(barrel_decl,type,
barrel: ( '$ki_world' * $i * $i ) > $o ).
tff(hollywood_decl,type,
hollywood: ( '$ki_world' * $i ) > $o ).
tff(city_decl,type,
city: ( '$ki_world' * $i ) > $o ).
tff(in_decl,type,
in: ( '$ki_world' * $i * $i ) > $o ).
tff(young_decl,type,
young: ( '$ki_world' * $i ) > $o ).
tff(old_decl,type,
old: ( '$ki_world' * $i ) > $o ).
tff(down_decl,type,
down: ( '$ki_world' * $i * $i ) > $o ).
tff(way_decl,type,
way: ( '$ki_world' * $i ) > $o ).
tff(qmltpeq_decl,type,
qmltpeq: ( '$ki_world' * $i * $i ) > $o ).
tff(seat_decl,type,
seat: ( '$ki_world' * $i ) > $o ).
tff(white_decl,type,
white: ( '$ki_world' * $i ) > $o ).
tff(car_decl,type,
car: ( '$ki_world' * $i ) > $o ).
tff(furniture_decl,type,
furniture: ( '$ki_world' * $i ) > $o ).
tff(street_decl,type,
street: ( '$ki_world' * $i ) > $o ).
tff(fellow_decl,type,
fellow: ( '$ki_world' * $i ) > $o ).
tff(front_decl,type,
front: ( '$ki_world' * $i ) > $o ).
tff(man_decl,type,
man: ( '$ki_world' * $i ) > $o ).
tff(event_decl,type,
event: ( '$ki_world' * $i ) > $o ).
tff(lonely_decl,type,
lonely: ( '$ki_world' * $i ) > $o ).
tff('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff('$ki_exists_in_world_$i_nonempty',axiom,
! [W: '$ki_world'] :
? [X: $i] : '$ki_exists_in_world_$i'(W,X) ).
tff(reflexivity,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [X: $i] :
( '$ki_exists_in_world_$i'(W,X)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,X,X) ) ) ) ).
tff(symmetry,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [X: $i] :
( '$ki_exists_in_world_$i'(W,X)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [Y: $i] :
( '$ki_exists_in_world_$i'(W0,Y)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,X,Y) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,Y,X) ) ) ) ) ) ) ) ).
tff(transitivity,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [X: $i] :
( '$ki_exists_in_world_$i'(W,X)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [Y: $i] :
( '$ki_exists_in_world_$i'(W0,Y)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ! [Z: $i] :
( '$ki_exists_in_world_$i'(W1,Z)
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> ( ( ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,X,Y) )
& ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,Y,Z) ) )
=> ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,X,Z) ) ) ) ) ) ) ) ) ) ).
tff(barrel_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W1,C)
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> ( ( ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,A,B) )
& ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> barrel(W3,A,C) ) )
=> ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> barrel(W3,B,C) ) ) ) ) ) ) ) ) ) ).
tff(barrel_substitution_2,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W1,C)
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> ( ( ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,A,B) )
& ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> barrel(W3,C,A) ) )
=> ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> barrel(W3,C,B) ) ) ) ) ) ) ) ) ) ).
tff(car_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> car(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> car(W2,B) ) ) ) ) ) ) ) ).
tff(chevy_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> chevy(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> chevy(W2,B) ) ) ) ) ) ) ) ).
tff(city_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> city(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> city(W2,B) ) ) ) ) ) ) ) ).
tff(dirty_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> dirty(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> dirty(W2,B) ) ) ) ) ) ) ) ).
tff(down_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W1,C)
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> ( ( ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,A,B) )
& ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> down(W3,A,C) ) )
=> ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> down(W3,B,C) ) ) ) ) ) ) ) ) ) ).
tff(down_substitution_2,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W1,C)
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> ( ( ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,A,B) )
& ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> down(W3,C,A) ) )
=> ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> down(W3,C,B) ) ) ) ) ) ) ) ) ) ).
tff(event_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> event(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> event(W2,B) ) ) ) ) ) ) ) ).
tff(fellow_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> fellow(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> fellow(W2,B) ) ) ) ) ) ) ) ).
tff(front_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> front(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> front(W2,B) ) ) ) ) ) ) ) ).
tff(furniture_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> furniture(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> furniture(W2,B) ) ) ) ) ) ) ) ).
tff(hollywood_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> hollywood(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> hollywood(W2,B) ) ) ) ) ) ) ) ).
tff(in_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W1,C)
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> ( ( ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,A,B) )
& ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> in(W3,A,C) ) )
=> ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> in(W3,B,C) ) ) ) ) ) ) ) ) ) ).
tff(in_substitution_2,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W1,C)
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> ( ( ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> qmltpeq(W3,A,B) )
& ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> in(W3,C,A) ) )
=> ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> in(W3,C,B) ) ) ) ) ) ) ) ) ) ).
tff(lonely_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> lonely(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> lonely(W2,B) ) ) ) ) ) ) ) ).
tff(man_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> man(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> man(W2,B) ) ) ) ) ) ) ) ).
tff(old_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> old(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> old(W2,B) ) ) ) ) ) ) ) ).
tff(seat_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> seat(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> seat(W2,B) ) ) ) ) ) ) ) ).
tff(street_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> street(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> street(W2,B) ) ) ) ) ) ) ) ).
tff(way_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> way(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> way(W2,B) ) ) ) ) ) ) ) ).
tff(white_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> white(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> white(W2,B) ) ) ) ) ) ) ) ).
tff(young_substitution_1,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [A: $i] :
( '$ki_exists_in_world_$i'(W,A)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W0,B)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> qmltpeq(W2,A,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> young(W2,A) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> young(W2,B) ) ) ) ) ) ) ) ).
tff(verify,conjecture,
( ! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ( ? [U: $i] :
( '$ki_exists_in_world_$i'(W,U)
& ? [V: $i] :
( '$ki_exists_in_world_$i'(W,V)
& ? [W: $i] :
( '$ki_exists_in_world_$i'(W,W)
& ? [X: $i] :
( '$ki_exists_in_world_$i'(W,X)
& ? [Y: $i] :
( '$ki_exists_in_world_$i'(W,Y)
& ? [Z: $i] :
( '$ki_exists_in_world_$i'(W,Z)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(W,X1)
& ? [X2: $i] :
( '$ki_exists_in_world_$i'(W,X2)
& ? [X3: $i] :
( '$ki_exists_in_world_$i'(W,X3)
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> hollywood(W0,U) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> city(W0,U) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> event(W0,V) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> street(W0,W) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> way(W0,W) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> lonely(W0,W) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> chevy(W0,X) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> car(W0,X) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> white(W0,X) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> dirty(W0,X) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> old(W0,X) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> barrel(W0,V,X) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> down(W0,V,W) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,V,U) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> seat(W0,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> furniture(W0,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> front(W0,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ~ ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> qmltpeq(W1,Y,Z) ) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> fellow(W0,Y) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> man(W0,Y) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> young(W0,Y) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> fellow(W0,Z) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> man(W0,Z) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> young(W0,Z) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,Y,X2) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X2,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,Z,X3) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X3,X1) ) ) ) ) ) ) ) ) ) )
=> ? [X4: $i] :
( '$ki_exists_in_world_$i'(W,X4)
& ? [X5: $i] :
( '$ki_exists_in_world_$i'(W,X5)
& ? [X6: $i] :
( '$ki_exists_in_world_$i'(W,X6)
& ? [X7: $i] :
( '$ki_exists_in_world_$i'(W,X7)
& ? [X8: $i] :
( '$ki_exists_in_world_$i'(W,X8)
& ? [X9: $i] :
( '$ki_exists_in_world_$i'(W,X9)
& ? [X10: $i] :
( '$ki_exists_in_world_$i'(W,X10)
& ? [X11: $i] :
( '$ki_exists_in_world_$i'(W,X11)
& ? [X12: $i] :
( '$ki_exists_in_world_$i'(W,X12)
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> hollywood(W0,X4) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> city(W0,X4) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> event(W0,X5) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> chevy(W0,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> car(W0,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> white(W0,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> dirty(W0,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> old(W0,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> street(W0,X7) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> way(W0,X7) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> lonely(W0,X7) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> barrel(W0,X5,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> down(W0,X5,X7) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X5,X4) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> seat(W0,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> furniture(W0,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> front(W0,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ~ ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> qmltpeq(W1,X8,X9) ) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> fellow(W0,X8) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> man(W0,X8) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> young(W0,X8) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> fellow(W0,X9) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> man(W0,X9) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> young(W0,X9) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,X8,X11) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X11,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,X9,X12) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X12,X10) ) ) ) ) ) ) ) ) ) ) ) )
& ! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ( ? [X13: $i] :
( '$ki_exists_in_world_$i'(W,X13)
& ? [X14: $i] :
( '$ki_exists_in_world_$i'(W,X14)
& ? [X15: $i] :
( '$ki_exists_in_world_$i'(W,X15)
& ? [X16: $i] :
( '$ki_exists_in_world_$i'(W,X16)
& ? [X17: $i] :
( '$ki_exists_in_world_$i'(W,X17)
& ? [X18: $i] :
( '$ki_exists_in_world_$i'(W,X18)
& ? [X19: $i] :
( '$ki_exists_in_world_$i'(W,X19)
& ? [X20: $i] :
( '$ki_exists_in_world_$i'(W,X20)
& ? [X21: $i] :
( '$ki_exists_in_world_$i'(W,X21)
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> hollywood(W0,X13) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> city(W0,X13) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> event(W0,X14) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> chevy(W0,X15) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> car(W0,X15) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> white(W0,X15) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> dirty(W0,X15) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> old(W0,X15) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> street(W0,X16) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> way(W0,X16) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> lonely(W0,X16) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> barrel(W0,X14,X15) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> down(W0,X14,X16) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X14,X13) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> seat(W0,X19) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> furniture(W0,X19) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> front(W0,X19) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ~ ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> qmltpeq(W1,X17,X18) ) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> fellow(W0,X17) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> man(W0,X17) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> young(W0,X17) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> fellow(W0,X18) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> man(W0,X18) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> young(W0,X18) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,X17,X20) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X20,X19) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,X18,X21) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X21,X19) ) ) ) ) ) ) ) ) ) )
=> ? [X22: $i] :
( '$ki_exists_in_world_$i'(W,X22)
& ? [X23: $i] :
( '$ki_exists_in_world_$i'(W,X23)
& ? [X24: $i] :
( '$ki_exists_in_world_$i'(W,X24)
& ? [X25: $i] :
( '$ki_exists_in_world_$i'(W,X25)
& ? [X26: $i] :
( '$ki_exists_in_world_$i'(W,X26)
& ? [X27: $i] :
( '$ki_exists_in_world_$i'(W,X27)
& ? [X28: $i] :
( '$ki_exists_in_world_$i'(W,X28)
& ? [X29: $i] :
( '$ki_exists_in_world_$i'(W,X29)
& ? [X30: $i] :
( '$ki_exists_in_world_$i'(W,X30)
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> hollywood(W0,X22) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> city(W0,X22) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> event(W0,X23) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> street(W0,X24) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> way(W0,X24) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> lonely(W0,X24) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> chevy(W0,X25) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> car(W0,X25) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> white(W0,X25) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> dirty(W0,X25) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> old(W0,X25) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> barrel(W0,X23,X25) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> down(W0,X23,X24) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X23,X22) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> seat(W0,X28) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> furniture(W0,X28) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> front(W0,X28) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ~ ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> qmltpeq(W1,X26,X27) ) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> fellow(W0,X26) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> man(W0,X26) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> young(W0,X26) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> fellow(W0,X27) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> man(W0,X27) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> young(W0,X27) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,X26,X29) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X29,X28) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> qmltpeq(W0,X27,X30) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X30,X28) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------