%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PLA054_4 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:20:02 AM UTC 2026
% Result : Theorem 20.33s 6.30s
% Output : Refutation 20.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 19 unt; 0 typ; 3 def)
% Number of atoms : 336 ( 19 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1056 ( 176 ~; 145 |; 38 &; 650 @)
% ( 0 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 170 ( 5 ^; 152 !; 10 ?; 170 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf('$ki_world_type',type,
'$ki_world': $tType ).
thf('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
thf('$ki_accessible_decl',type,
'$ki_accessible': '$ki_world' > '$ki_world' > $o ).
thf(d_decl,type,
d: $i ).
thf(o_decl,type,
o: $i ).
thf(h_decl,type,
h: '$ki_world' > $i > $o ).
thf(closed_decl,type,
closed: '$ki_world' > $i > $o ).
thf(combo_decl,type,
combo: '$ki_world' > $i > $i > $o ).
thf(open_decl,type,
open: '$ki_world' > $i > $o ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(sk1_decl,type,
sk1: '$ki_world' ).
thf(sk2_decl,type,
sk2: $i > $i > '$ki_world' ).
thf(sk4_decl,type,
sk4: $i > $i > '$ki_world' > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: '$ki_world'] :
~ ( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ? [C: $i] :
( ( ! [D: '$ki_world'] :
( ( D @ ( A @ '$ki_accessible' ) )
=> ( ( C @ ( D @ h ) )
& ( B @ ( d @ ( D @ combo ) ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( A @ '$ki_accessible' ) )
=> ( d @ ( D @ open ) ) ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: '$ki_world'] :
~ ( ( C @ ( sk1 @ '$ki_accessible' ) )
=> ( d @ ( C @ open ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: '$ki_world'] :
@+[D: $i] :
( ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ( o @ ( E @ h ) )
& ~ ( A @ ( B @ ( E @ combo ) ) )
& ( B @ ( E @ closed ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ closed ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ( ( D @ ( E @ h ) )
& ( A @ ( B @ ( E @ combo ) ) )
& ( B @ ( E @ closed ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ open ) ) ) ) )
& ( D @ ( C @ '$ki_exists_in_world_$i' ) ) ) ) ) ).
thf(3,axiom,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(19,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(cnf,[status(esa)],[19]) ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ? [C: $i] :
( ( ! [D: '$ki_world'] :
( ( D @ ( A @ '$ki_accessible' ) )
=> ( ( C @ ( D @ h ) )
& ( B @ ( d @ ( D @ combo ) ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( A @ '$ki_accessible' ) )
=> ( d @ ( D @ open ) ) ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ? [C: $i] :
( ( ! [D: '$ki_world'] :
( ( D @ ( A @ '$ki_accessible' ) )
=> ( ( C @ ( D @ h ) )
& ( B @ ( d @ ( D @ combo ) ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( A @ '$ki_accessible' ) )
=> ( d @ ( D @ open ) ) ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ? [C: $i] :
( ( ! [D: '$ki_world'] :
( ( D @ ( A @ '$ki_accessible' ) )
=> ( ( C @ ( D @ h ) )
& ( B @ ( d @ ( D @ combo ) ) ) ) )
=> ! [D: '$ki_world'] :
( ( D @ ( A @ '$ki_accessible' ) )
=> ( d @ ( D @ open ) ) ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
! [C: '$ki_world',B: $i,A: $i] :
( ( ~ ( d @ ( A @ ( B @ sk2 ) @ open ) )
| ~ ( B @ ( sk1 @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( sk1 @ '$ki_exists_in_world_$i' ) ) )
& ( ( A @ ( B @ sk2 ) @ ( sk1 @ '$ki_accessible' ) )
| ~ ( B @ ( sk1 @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( sk1 @ '$ki_exists_in_world_$i' ) ) )
& ( ( B @ ( C @ h ) )
| ~ ( C @ ( sk1 @ '$ki_accessible' ) )
| ~ ( B @ ( sk1 @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( sk1 @ '$ki_exists_in_world_$i' ) ) )
& ( ( A @ ( d @ ( C @ combo ) ) )
| ~ ( C @ ( sk1 @ '$ki_accessible' ) )
| ~ ( B @ ( sk1 @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( sk1 @ '$ki_exists_in_world_$i' ) ) )
& ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(17,plain,
! [C: '$ki_world',B: $i,A: $i] :
( ( A @ ( d @ ( C @ combo ) ) )
| ~ ( C @ ( sk1 @ '$ki_accessible' ) )
| ~ ( B @ ( sk1 @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( sk1 @ '$ki_exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(5,axiom,
! [A: '$ki_world',B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
thf(23,plain,
! [A: '$ki_world',B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
! [B: $i,A: '$ki_world'] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(cnf,[status(esa)],[23]) ).
thf(111,plain,
! [B: '$ki_world',A: $i] :
( ( A @ ( d @ ( B @ combo ) ) )
| ~ ( B @ ( sk1 @ '$ki_accessible' ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[17,24]) ).
thf(112,plain,
! [B: '$ki_world',A: $i] :
( ( A @ ( d @ ( B @ combo ) ) )
| ~ ( B @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(115,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( C @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ ( d @ ( C @ combo ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,112]) ).
thf(116,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( C @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ ( d @ ( C @ combo ) ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(117,plain,
! [A: $i] : ( A @ ( d @ ( sk1 @ combo ) ) ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( sk1 )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(122,plain,
! [A: $i] : ( A @ ( d @ ( sk1 @ combo ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(7,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: $i] :
( ( C @ ( A @ '$ki_exists_in_world_$i' ) )
=> ? [D: $i] :
( ! [E: '$ki_world'] :
( ( E @ ( A @ '$ki_accessible' ) )
=> ( ( ( o @ ( E @ h ) )
& ~ ( C @ ( B @ ( E @ combo ) ) )
& ( B @ ( E @ closed ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ closed ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( A @ '$ki_accessible' ) )
=> ( ( ( D @ ( E @ h ) )
& ( C @ ( B @ ( E @ combo ) ) )
& ( B @ ( E @ closed ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ open ) ) ) ) )
& ( D @ ( A @ '$ki_exists_in_world_$i' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(27,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: $i] :
( ( C @ ( A @ '$ki_exists_in_world_$i' ) )
=> ? [D: $i] :
( ! [E: '$ki_world'] :
( ( E @ ( A @ '$ki_accessible' ) )
=> ( ( ( o @ ( E @ h ) )
& ~ ( C @ ( B @ ( E @ combo ) ) )
& ( B @ ( E @ closed ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ closed ) ) ) ) )
& ! [E: '$ki_world'] :
( ( E @ ( A @ '$ki_accessible' ) )
=> ( ( ( D @ ( E @ h ) )
& ( C @ ( B @ ( E @ combo ) ) )
& ( B @ ( E @ closed ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( F @ open ) ) ) ) )
& ( D @ ( A @ '$ki_exists_in_world_$i' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,plain,
! [G: '$ki_world',F: '$ki_world',E: '$ki_world',D: '$ki_world',C: $i,B: $i,A: '$ki_world'] :
( ( ( B @ ( G @ closed ) )
| ~ ( G @ ( F @ '$ki_accessible' ) )
| ~ ( o @ ( F @ h ) )
| ( C @ ( B @ ( F @ combo ) ) )
| ~ ( B @ ( F @ closed ) )
| ~ ( F @ ( A @ '$ki_accessible' ) )
| ~ ( C @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( B @ ( E @ open ) )
| ~ ( E @ ( D @ '$ki_accessible' ) )
| ~ ( A @ ( B @ ( C @ sk4 ) ) @ ( D @ h ) )
| ~ ( C @ ( B @ ( D @ combo ) ) )
| ~ ( B @ ( D @ closed ) )
| ~ ( D @ ( A @ '$ki_accessible' ) )
| ~ ( C @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( C @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(30,plain,
! [E: '$ki_world',D: '$ki_world',C: $i,B: $i,A: '$ki_world'] :
( ( B @ ( E @ open ) )
| ~ ( E @ ( D @ '$ki_accessible' ) )
| ~ ( A @ ( B @ ( C @ sk4 ) ) @ ( D @ h ) )
| ~ ( C @ ( B @ ( D @ combo ) ) )
| ~ ( B @ ( D @ closed ) )
| ~ ( D @ ( A @ '$ki_accessible' ) )
| ~ ( C @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(340,plain,
! [E: '$ki_world',D: '$ki_world',C: $i,B: $i,A: '$ki_world'] :
( ( B @ ( E @ open ) )
| ~ ( E @ ( D @ '$ki_accessible' ) )
| ~ ( A @ ( B @ ( C @ sk4 ) ) @ ( D @ h ) )
| ~ ( C @ ( B @ ( D @ combo ) ) )
| ~ ( B @ ( D @ closed ) )
| ~ ( D @ ( A @ '$ki_accessible' ) )
| ~ $true
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(rewrite,[status(thm)],[30,24]) ).
thf(341,plain,
! [E: '$ki_world',D: '$ki_world',C: $i,B: $i,A: '$ki_world'] :
( ( B @ ( E @ open ) )
| ~ ( E @ ( D @ '$ki_accessible' ) )
| ~ ( A @ ( B @ ( C @ sk4 ) ) @ ( D @ h ) )
| ~ ( C @ ( B @ ( D @ combo ) ) )
| ~ ( B @ ( D @ closed ) )
| ~ ( D @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(384,plain,
! [F: '$ki_world',E: '$ki_world',D: $i,C: $i,B: '$ki_world',A: $i] :
( ( ( A @ ( d @ ( sk1 @ combo ) ) )
!= ( D @ ( C @ ( E @ combo ) ) ) )
| ( C @ ( F @ open ) )
| ~ ( F @ ( E @ '$ki_accessible' ) )
| ~ ( B @ ( C @ ( D @ sk4 ) ) @ ( E @ h ) )
| ~ $true
| ~ ( C @ ( E @ closed ) )
| ~ ( E @ ( B @ '$ki_accessible' ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[122,341]) ).
thf(385,plain,
! [F: '$ki_world',E: '$ki_world',D: $i,C: $i,B: '$ki_world',A: $i] :
( ( ( A @ ( d @ ( sk1 @ combo ) ) )
!= ( D @ ( C @ ( E @ combo ) ) ) )
| ( C @ ( F @ open ) )
| ~ ( F @ ( E @ '$ki_accessible' ) )
| ~ ( B @ ( C @ ( D @ sk4 ) ) @ ( E @ h ) )
| ~ ( C @ ( E @ closed ) )
| ~ ( E @ ( B @ '$ki_accessible' ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(386,plain,
! [C: '$ki_world',B: '$ki_world',A: $i] :
( ( d @ ( C @ open ) )
| ~ ( C @ ( sk1 @ '$ki_accessible' ) )
| ~ ( B @ ( d @ ( A @ sk4 ) ) @ ( sk1 @ h ) )
| ~ ( d @ ( sk1 @ closed ) )
| ~ ( sk1 @ ( B @ '$ki_accessible' ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( d )),bind(D,$thf( A )),bind(E,$thf( sk1 ))]]) ).
thf(447,plain,
! [C: '$ki_world',B: '$ki_world',A: $i] :
( ( d @ ( C @ open ) )
| ~ ( C @ ( sk1 @ '$ki_accessible' ) )
| ~ ( B @ ( d @ ( A @ sk4 ) ) @ ( sk1 @ h ) )
| ~ ( d @ ( sk1 @ closed ) )
| ~ ( sk1 @ ( B @ '$ki_accessible' ) )
| ~ ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(15,plain,
sk1 @ ( '$ki_local_world' @ '$ki_accessible' ),
inference(cnfConj,[status(thm)],[13]) ).
thf(8,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( d @ ( A @ closed ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(33,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( d @ ( A @ closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(34,plain,
! [A: '$ki_world'] :
( ( d @ ( A @ closed ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(80,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( d @ ( A @ closed ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,34]) ).
thf(81,plain,
! [A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ( d @ ( A @ closed ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
d @ ( sk1 @ closed ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( sk1 ))]]) ).
thf(16,plain,
! [C: '$ki_world',B: $i,A: $i] :
( ( B @ ( C @ h ) )
| ~ ( C @ ( sk1 @ '$ki_accessible' ) )
| ~ ( B @ ( sk1 @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( sk1 @ '$ki_exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(62,plain,
! [B: '$ki_world',A: $i] :
( ( A @ ( B @ h ) )
| ~ ( B @ ( sk1 @ '$ki_accessible' ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[16,24]) ).
thf(63,plain,
! [B: '$ki_world',A: $i] :
( ( A @ ( B @ h ) )
| ~ ( B @ ( sk1 @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(66,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( C @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ ( C @ h ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,63]) ).
thf(67,plain,
! [C: '$ki_world',B: $i,A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( C @ ( sk1 @ '$ki_accessible' ) ) )
| ( B @ ( C @ h ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
! [A: $i] : ( A @ ( sk1 @ h ) ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(73,plain,
! [A: $i] : ( A @ ( sk1 @ h ) ),
inference(simp,[status(thm)],[68]) ).
thf(4901,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( d @ ( B @ open ) )
| ~ ( B @ ( sk1 @ '$ki_accessible' ) )
| ~ $true
| ~ $true
| ~ ( sk1 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(rewrite,[status(thm)],[447,82,73]) ).
thf(4902,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( d @ ( B @ open ) )
| ~ ( B @ ( sk1 @ '$ki_accessible' ) )
| ~ ( sk1 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[4901]) ).
thf(10,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ~ ( ( B @ ( A @ closed ) )
& ( B @ ( A @ open ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(36,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ~ ( ( B @ ( A @ closed ) )
& ( B @ ( A @ open ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,plain,
! [B: $i,A: '$ki_world'] :
( ~ ( B @ ( A @ closed ) )
| ~ ( B @ ( A @ open ) )
| ~ ( B @ ( A @ '$ki_exists_in_world_$i' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(45,plain,
! [B: $i,A: '$ki_world'] :
( ~ ( B @ ( A @ closed ) )
| ~ ( B @ ( A @ open ) )
| ~ $true
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(rewrite,[status(thm)],[37,24]) ).
thf(46,plain,
! [B: $i,A: '$ki_world'] :
( ~ ( B @ ( A @ closed ) )
| ~ ( B @ ( A @ open ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(47,plain,
! [B: $i,A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( B @ ( A @ closed ) )
| ~ ( B @ ( A @ open ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15,46]) ).
thf(48,plain,
! [B: $i,A: '$ki_world'] :
( ( ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) )
!= ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( B @ ( A @ closed ) )
| ~ ( B @ ( A @ open ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ closed ) )
| ~ ( A @ ( sk1 @ open ) ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk1 ))]]) ).
thf(53,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ closed ) )
| ~ ( A @ ( sk1 @ open ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(77,plain,
! [B: $i,A: '$ki_world'] :
( ( ( d @ ( A @ closed ) )
!= ( B @ ( sk1 @ closed ) ) )
| ~ $true
| ~ ( B @ ( sk1 @ open ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[34,53]) ).
thf(78,plain,
! [B: $i,A: '$ki_world'] :
( ( ( d @ ( A @ closed ) )
!= ( B @ ( sk1 @ closed ) ) )
| ~ ( B @ ( sk1 @ open ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
( ~ ( d @ ( sk1 @ open ) )
| ~ ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( sk1 )),bind(B,$thf( d ))]]) ).
thf(94,plain,
( ~ ( d @ ( sk1 @ open ) )
| ~ $true ),
inference(rewrite,[status(thm)],[79,15]) ).
thf(95,plain,
~ ( d @ ( sk1 @ open ) ),
inference(simp,[status(thm)],[94]) ).
thf(5034,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( d @ ( B @ open ) )
!= ( d @ ( sk1 @ open ) ) )
| ~ $true
| ~ ( B @ ( sk1 @ '$ki_accessible' ) )
| ~ ( sk1 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(paramod_ordered,[status(thm)],[4902,95]) ).
thf(5035,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( d @ ( B @ open ) )
!= ( d @ ( sk1 @ open ) ) )
| ~ ( B @ ( sk1 @ '$ki_accessible' ) )
| ~ ( sk1 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5034]) ).
thf(5036,plain,
! [A: '$ki_world'] :
( ~ ( sk1 @ ( sk1 @ '$ki_accessible' ) )
| ~ ( sk1 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(pattern_uni,[status(thm)],[5035:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(5087,plain,
! [A: '$ki_world'] :
( ~ ( sk1 @ ( sk1 @ '$ki_accessible' ) )
| ~ ( sk1 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5036]) ).
thf(5133,plain,
! [A: '$ki_world'] :
( ~ $true
| ~ ( sk1 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(rewrite,[status(thm)],[5087,20]) ).
thf(5134,plain,
! [A: '$ki_world'] :
( ~ ( sk1 @ ( A @ '$ki_accessible' ) )
| ~ ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5133]) ).
thf(5146,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( sk1 @ ( B @ '$ki_accessible' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,5134]) ).
thf(5147,plain,
! [B: '$ki_world',A: '$ki_world'] :
( ( ( A @ ( A @ '$ki_accessible' ) )
!= ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
| ~ ( sk1 @ ( B @ '$ki_accessible' ) ) ),
inference(simp,[status(thm)],[5146]) ).
thf(5148,plain,
~ ( sk1 @ ( '$ki_local_world' @ '$ki_accessible' ) ),
inference(pattern_uni,[status(thm)],[5147:[bind(A,$thf( '$ki_local_world' )),bind(B,$thf( '$ki_local_world' ))]]) ).
thf(5233,plain,
~ $true,
inference(rewrite,[status(thm)],[5148,15]) ).
thf(5234,plain,
$false,
inference(simp,[status(thm)],[5233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA054_4 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.41 % Computer : n010.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sat Sep 26 04:53:15 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.20 % [INFO] Parsing done (207ms).
% 1.40/1.22 % [INFO] Running in sequential loop mode.
% 2.18/1.62 % [INFO] eprover registered as external prover.
% 2.18/1.63 % [INFO] Scanning for conjecture ...
% 2.38/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 2.38/1.79 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.57/1.83 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.57/1.84 % [INFO] Type checking passed.
% 2.57/1.84 % [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 ...
% 19.88/6.29 % [INFO] Killing All external provers ...
% 20.33/6.30 % Time passed: 5742ms (effective reasoning time: 5071ms)
% 20.33/6.30 % 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)>
% 20.33/6.30 % Axioms used in derivation (5): ax4, mrel_reflexive, ax1, ax2, $ki_exists_in_world_$i_const
% 20.33/6.30 % No. of inferences in proof: 68
% 20.33/6.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5742 ms resp. 5071 ms w/o parsing
% 20.33/6.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.33/6.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------