TSTP Solution File: LCL947_10 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : LCL947_10 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:08:47 EDT 2024
% Result : Theorem 6.64s 2.77s
% Output : Refutation 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 50 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 453 ( 0 equ; 0 cnn)
% Maximal formula atoms : 34 ( 10 avg)
% Number of connectives : 1470 ( 2 ~; 4 |; 28 &;1057 @)
% ( 0 <=>; 379 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 17 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 343 ( 0 ^ 341 !; 2 ?; 343 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'$ki_world\'_type',type,
'\'$ki_world\'': $tType ).
thf('\'$ki_local_world\'_type',type,
'\'$ki_local_world\'': '\'$ki_world\'' ).
thf('\'$ki_accessible\'_type',type,
'\'$ki_accessible\'': '\'$ki_world\'' > '\'$ki_world\'' > $o ).
thf(qmltpeq_type,type,
qmltpeq: '\'$ki_world\'' > $i > $i > $o ).
thf(member_type,type,
member: '\'$ki_world\'' > $i > $i > $o ).
thf(subset_type,type,
subset: '\'$ki_world\'' > $i > $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf('\'$ki_exists_in_world_$i\'_type',type,
'\'$ki_exists_in_world_$i\'': '\'$ki_world\'' > $i > $o ).
thf(12,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( subset @ H @ B @ F ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( subset @ H @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(101,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( subset @ H @ B @ F ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( subset @ H @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(106,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ D @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ( ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) ) ) ) ) ) ) )
& ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) ) ) ) ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(129,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ( ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) ) ) ) ) ) ) )
& ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) ) ) ) ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( qmltpeq @ E @ ( union @ B @ D ) @ ( union @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(91,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( qmltpeq @ E @ ( union @ B @ D ) @ ( union @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ B ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(114,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ B ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ ( union @ F @ B ) @ ( union @ F @ D ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).
thf(119,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ ( union @ F @ B ) @ ( union @ F @ D ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(146,plain,
! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(7,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ( ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) ) ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) ) ) ) ) ) ) ) )
& ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) ) ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) ) ) ) ) ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(47,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ( ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) ) ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) ) ) ) ) ) ) ) )
& ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ! [G: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) ) ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ F @ H )
=> ( ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ D ) )
=> ! [I: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ H @ I )
=> ( member @ I @ G @ B ) ) ) ) ) ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ B @ F ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(93,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ B @ F ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ D @ F ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(29,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ D @ F ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( qmltpeq @ C @ B @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(109,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( qmltpeq @ C @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( subset @ H @ F @ B ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( subset @ H @ F @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(124,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
& ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( subset @ H @ F @ B ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( subset @ H @ F @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ( ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ ( union @ B @ D ) ) )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ B ) )
| ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ D ) ) ) ) )
& ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ B ) )
| ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ D ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ ( union @ B @ D ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(34,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ( ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ ( union @ B @ D ) ) )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ B ) )
| ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ D ) ) ) ) )
& ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ B ) )
| ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ D ) ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( member @ H @ F @ ( union @ B @ D ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(45,plain,
! [A: '\'$ki_world\''] :
? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( qmltpeq @ C @ ( union @ B @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( qmltpeq @ C @ ( union @ B @ B ) @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( qmltpeq @ C @ ( union @ B @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: '\'$ki_world\''] :
( ( ( '\'$ki_accessible\'' @ A @ B )
& ( '\'$ki_accessible\'' @ B @ C ) )
=> ( '\'$ki_accessible\'' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(27,plain,
! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: '\'$ki_world\''] :
( ( ( '\'$ki_accessible\'' @ A @ B )
& ( '\'$ki_accessible\'' @ B @ C ) )
=> ( '\'$ki_accessible\'' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ( ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ D @ B ) ) ) ) )
& ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ D @ B ) ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(76,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ( ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ D @ B ) ) ) ) )
& ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) )
& ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ D @ B ) ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ ( union @ B @ D ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
thf(98,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ( ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( subset @ F @ B @ D ) )
=> ! [F: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ F )
=> ( qmltpeq @ F @ ( union @ B @ D ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ ( union @ B @ F ) @ ( union @ D @ F ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).
thf(111,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ! [D: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
=> ! [E: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ C @ E )
=> ! [F: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
=> ! [G: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ E @ G )
=> ( ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ B @ D ) )
=> ! [H: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ G @ H )
=> ( qmltpeq @ H @ ( union @ B @ F ) @ ( union @ D @ F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( subset @ C @ B @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(122,plain,
! [A: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
=> ! [B: $i] :
( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
=> ! [C: '\'$ki_world\''] :
( ( '\'$ki_accessible\'' @ A @ C )
=> ( subset @ C @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(209,plain,
$false,
inference(e,[status(thm)],[101,106,129,91,114,119,146,47,93,29,109,124,34,45,22,27,76,98,111,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : LCL947_10 : TPTP v8.2.0. Released v8.2.0.
% 0.11/0.17 % Command : run_Leo-III %s %d
% 0.15/0.38 % Computer : n022.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Mon May 20 01:50:09 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.96/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.08 % [INFO] Parsing done (162ms).
% 1.49/1.09 % [INFO] Running in sequential loop mode.
% 1.92/1.33 % [INFO] eprover registered as external prover.
% 1.92/1.33 % [INFO] cvc4 registered as external prover.
% 1.92/1.34 % [INFO] Scanning for conjecture ...
% 2.11/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.38/1.47 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.62/1.57 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.62/1.59 % [INFO] Type checking passed.
% 2.62/1.59 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.64/2.76 % External prover 'e' found a proof!
% 6.64/2.76 % [INFO] Killing All external provers ...
% 6.64/2.76 % Time passed: 2230ms (effective reasoning time: 1669ms)
% 6.64/2.76 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.64/2.77 % Axioms used in derivation (19): member_substitution_1, equal_member_defn, union_substitution_2, subset_union, member_substitution_2, symmetry, reflexivity_of_subset, $ki_exists_in_world_$i_nonempty, mrel_reflexive, subset_substitution_2, reflexivity, commutativity_of_union, subset_substitution_1, union_substitution_1, mrel_transitive, equal_defn, transitivity, union_defn, subset_defn
% 6.64/2.77 % No. of inferences in proof: 42
% 6.64/2.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2230 ms resp. 1669 ms w/o parsing
% 7.01/2.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.01/2.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------