TPTP Problem File: LCL945_9.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : LCL945_9 : TPTP v8.2.0. Released v8.2.0.
% Domain : Natural Language Processing
% Problem : Goedel translation of NLP001+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 : GNL001+1 [QMLTP]
% Status : Theorem
% Rating : 1.00 v8.2.0
% Syntax : Number of formulae : 21 ( 2 unt; 18 typ; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 130 ( 44 avg)
% Number of connectives : 129 ( 0 ~; 0 |; 69 &)
% ( 0 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 35 ( 16 >; 19 *; 0 +; 0 <<)
% Number of predicates : 16 ( 16 usr; 0 prp; 2-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 78 (; 60 !; 18 ?; 78 :)
% SPC : TF0_THM_NEQ_NAR
% Comments : Generated by embedproblem, version 1.7.14, rigid constant,
% modal_system_D, 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' ) > $o ).
tff(mrel_serial,axiom,
! [W: '$ki_world'] :
? [V: '$ki_world'] : '$ki_accessible'(W,V) ).
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 ) > $o ).
tff(old_decl,type,
old: ( '$ki_world' * $i ) > $o ).
tff(down_decl,type,
down: ( '$ki_world' * $i * $i ) > $o ).
tff(way_decl,type,
way: ( '$ki_world' * $i ) > $o ).
tff(white_decl,type,
white: ( '$ki_world' * $i ) > $o ).
tff(car_decl,type,
car: ( '$ki_world' * $i ) > $o ).
tff(street_decl,type,
street: ( '$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_$i'(W,X) ).
tff(verify,conjecture,
( ! [W: '$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_$i'(W,X)
& ! [W0: '$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) ) ) ) ) )
=> ? [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_$i'(W,X2)
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> hollywood(W0,Y) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> city(W0,Y) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> event(W0,Z) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> chevy(W0,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> car(W0,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> white(W0,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> dirty(W0,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> old(W0,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> street(W0,X2) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> way(W0,X2) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> lonely(W0,X2) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> barrel(W0,Z,X1) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> down(W0,Z,X2) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,Z,Y) ) ) ) ) ) ) )
& ! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ( ? [X3: $i] :
( '$ki_exists_in_world_$i'(W,X3)
& ? [X4: $i] :
( '$ki_exists_in_world_$i'(W,X4)
& ? [X5: $i] :
( '$ki_exists_in_world_$i'(W,X5)
& ? [X6: $i] :
( '$ki_exists_in_world_$i'(W,X6)
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> hollywood(W0,X3) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> city(W0,X3) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> event(W0,X4) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> chevy(W0,X5) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> car(W0,X5) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> white(W0,X5) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> dirty(W0,X5) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> old(W0,X5) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> street(W0,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> way(W0,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> lonely(W0,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> barrel(W0,X4,X5) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> down(W0,X4,X6) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X4,X3) ) ) ) ) )
=> ? [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_$i'(W,X10)
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> hollywood(W0,X7) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> city(W0,X7) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> event(W0,X8) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> street(W0,X9) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> way(W0,X9) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> lonely(W0,X9) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> chevy(W0,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> car(W0,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> white(W0,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> dirty(W0,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> old(W0,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> barrel(W0,X8,X10) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> down(W0,X8,X9) )
& ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> in(W0,X8,X7) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------