TPTP Problem File: LCL950_17.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% Domain : Set Theory
% Problem : Goedel translation of SET574+3
% 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 : GSE574+1 [QMLTP]
% Status : Theorem
% Rating : 0.00 v8.2.0
% Syntax : Number of formulae : 12 ( 3 unt; 6 typ; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 39 ( 0 ~; 0 |; 6 &)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 4 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 4 usr; 0 prp; 2-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 37 (; 34 !; 3 ?; 37 :)
% SPC : TF0_THM_NEQ_NAR
% Comments : Generated by embedproblem, version 1.7.14, rigid constant,
% modal_system_S5, 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' ) > $o ).
tff(mrel_universal,axiom,
! [W: '$ki_world',V: '$ki_world'] : '$ki_accessible'(W,V) ).
tff(intersect_decl,type,
intersect: ( '$ki_world' * $i * $i ) > $o ).
tff(member_decl,type,
member: ( '$ki_world' * $i * $i ) > $o ).
tff('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff('$ki_exists_in_world_$i_const',axiom,
! [W: '$ki_world',X: $i] : '$ki_exists_in_world_$i'(W,X) ).
tff('$ki_exists_in_world_$i_nonempty',axiom,
! [W: '$ki_world'] :
? [X: $i] : '$ki_exists_in_world_$i'(W,X) ).
tff(intersect_defn,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W,B)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W0,C)
=> ( ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> intersect(W2,B,C) )
=> ? [D: $i] :
( '$ki_exists_in_world_$i'(W1,D)
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> member(W2,D,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> member(W2,D,C) ) ) ) )
& ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ? [D: $i] :
( '$ki_exists_in_world_$i'(W1,D)
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> member(W2,D,B) )
& ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> member(W2,D,C) ) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> intersect(W2,B,C) ) ) ) ) ) ) ) ) ).
tff(symmetry_of_intersect,axiom,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W,B)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W0,C)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ( ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> intersect(W2,B,C) )
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> intersect(W2,C,B) ) ) ) ) ) ) ) ).
tff(verify,conjecture,
! [W: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',W)
=> ! [B: $i] :
( '$ki_exists_in_world_$i'(W,B)
=> ! [W0: '$ki_world'] :
( '$ki_accessible'(W,W0)
=> ! [C: $i] :
( '$ki_exists_in_world_$i'(W0,C)
=> ! [W1: '$ki_world'] :
( '$ki_accessible'(W0,W1)
=> ! [D: $i] :
( '$ki_exists_in_world_$i'(W1,D)
=> ! [W2: '$ki_world'] :
( '$ki_accessible'(W1,W2)
=> ( ( ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> member(W3,B,C) )
& ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> member(W3,B,D) ) )
=> ! [W3: '$ki_world'] :
( '$ki_accessible'(W2,W3)
=> intersect(W3,C,D) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------