%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO955_1 : TPTP v9.3.1. Released v9.1.0.
% 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 : n015.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 09:45:48 AM UTC 2026
% Result : Theorem 15.77s 5.50s
% Output : Refutation 15.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 9
% Syntax : Number of formulae : 132 ( 16 unt; 0 typ; 8 def)
% Number of atoms : 712 ( 62 equ; 0 cnn)
% Maximal formula atoms : 60 ( 5 avg)
% Number of connectives : 1957 ( 335 ~; 392 |; 38 &;1158 @)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 166 ( 4 ^; 136 !; 18 ?; 166 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(p_decl,type,
p: '$world' > $i > $o ).
thf('$exists_in_world_$i_decl',type,
'$exists_in_world_$i': '$world' > $i > $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i > '$world' ).
thf(sk3_decl,type,
sk3: '$world' > $i ).
thf(sk4_decl,type,
sk4: '$world' ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: '$world' > $i ).
thf(sk7_decl,type,
sk7: $i > '$world' ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: '$world' ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: '$world'] :
~ ( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: '$world'] :
@+[B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: '$world'] :
@+[B: $i] :
~ ( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: '$world'] :
~ ( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) ) ) ) ) ).
thf(1,conjecture,
( ( ? [A: $i] :
( ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) ) ) )
<=> ( ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
=> ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence14) ).
thf(2,negated_conjecture,
~ ( ( ? [A: $i] :
( ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) ) ) )
<=> ( ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
=> ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( ( ( ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
=> ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) ) )
=> ( ? [A: $i] :
( ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) ) ) ) )
& ( ( ? [A: $i] :
( ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) ) ) )
=> ( ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
=> ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [H: $i,G: '$world',F: $i,E: '$world',D: '$world',C: $i,B: '$world',A: $i] :
( ( ~ ( H @ ( sk9 @ p ) )
| ~ ( H @ ( sk9 @ '$exists_in_world_$i' ) )
| sk1 )
& ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( ( sk8 @ ( G @ p ) )
| ~ ( G @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 )
& ( ~ ( F @ ( F @ sk7 @ p ) )
| ~ ( F @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( E @ sk6 @ ( E @ p ) )
| ~ ( E @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( ( F @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( F @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( E @ sk6 @ ( E @ p ) )
| ~ ( E @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( ~ ( F @ ( F @ sk7 @ p ) )
| ~ ( F @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( E @ sk6 @ ( E @ '$exists_in_world_$i' ) )
| ~ ( E @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( ( F @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( F @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( E @ sk6 @ ( E @ '$exists_in_world_$i' ) )
| ~ ( E @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( ~ sk1
| ( sk5 @ ( D @ p ) )
| ~ ( D @ ( '$local_world' @ '$accessible_world' ) ) )
& ( ~ sk1
| ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
& ( ~ sk1
| ~ ( C @ ( sk4 @ p ) )
| ~ ( C @ ( sk4 @ '$exists_in_world_$i' ) ) )
& ( ~ sk1
| ( sk4 @ ( '$local_world' @ '$accessible_world' ) ) )
& ( ~ sk1
| ( B @ sk3 @ ( B @ p ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
& ( ~ sk1
| ( B @ sk3 @ ( B @ '$exists_in_world_$i' ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
& ( ~ sk1
| ( B @ sk3 @ ( B @ p ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
& ( ~ sk1
| ( B @ sk3 @ ( B @ '$exists_in_world_$i' ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(21,plain,
( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(6,plain,
( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(16,plain,
! [B: $i,A: '$world'] :
( ( B @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(27,plain,
! [B: $i,A: '$world'] :
( ( B @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[16]) ).
thf(912,plain,
! [B: $i,A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( B @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[6,27]) ).
thf(913,plain,
! [B: $i,A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( B @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| sk1 ),
inference(simp,[status(thm)],[912]) ).
thf(914,plain,
! [A: $i] :
( ( A @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( sk9 @ sk6 @ ( sk9 @ p ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( sk9 ))]]) ).
thf(948,plain,
! [A: $i] :
( ( A @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( sk9 @ sk6 @ ( sk9 @ p ) )
| sk1 ),
inference(simp,[status(thm)],[914]) ).
thf(978,plain,
! [A: $i] :
( ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( A @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ $true
| ( sk9 @ sk6 @ ( sk9 @ p ) )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[21,948]) ).
thf(979,plain,
! [A: $i] :
( ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( A @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ( sk9 @ sk6 @ ( sk9 @ p ) )
| sk1 ),
inference(simp,[status(thm)],[978]) ).
thf(980,plain,
( ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ( sk9 @ sk6 @ ( sk9 @ p ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[979:[bind(A,$thf( sk8 ))]]) ).
thf(12,plain,
! [B: $i,A: '$world'] :
( ( B @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(25,plain,
! [B: $i,A: '$world'] :
( ( B @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[12]) ).
thf(304,plain,
! [B: $i,A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( B @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[6,25]) ).
thf(305,plain,
! [B: $i,A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( B @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| sk1 ),
inference(simp,[status(thm)],[304]) ).
thf(306,plain,
! [A: $i] :
( ( A @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( sk9 ))]]) ).
thf(316,plain,
! [A: $i] :
( ( A @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) )
| sk1 ),
inference(simp,[status(thm)],[306]) ).
thf(437,plain,
! [A: $i] :
( ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( A @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ~ $true
| ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[21,316]) ).
thf(438,plain,
! [A: $i] :
( ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( A @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) )
| sk1 ),
inference(simp,[status(thm)],[437]) ).
thf(439,plain,
( ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[438:[bind(A,$thf( sk8 ))]]) ).
thf(17,plain,
! [A: $i] :
( ~ ( A @ ( sk9 @ p ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(24,plain,
! [A: $i] :
( ~ ( A @ ( sk9 @ p ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) )
| sk1 ),
inference(simp,[status(thm)],[17]) ).
thf(460,plain,
! [A: $i] :
( ( ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) )
!= ( A @ ( sk9 @ '$exists_in_world_$i' ) ) )
| ~ ( A @ ( sk9 @ p ) )
| ~ $true
| sk1
| ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(paramod_ordered,[status(thm)],[439,24]) ).
thf(461,plain,
! [A: $i] :
( ( ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) )
!= ( A @ ( sk9 @ '$exists_in_world_$i' ) ) )
| ~ ( A @ ( sk9 @ p ) )
| ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[460]) ).
thf(462,plain,
( ~ ( sk9 @ sk6 @ ( sk9 @ p ) )
| ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[461:[bind(A,$thf( sk9 @ sk6 ))]]) ).
thf(998,plain,
( ( ( sk9 @ sk6 @ ( sk9 @ p ) )
!= ( sk9 @ sk6 @ ( sk9 @ p ) ) )
| ~ $true
| ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| sk1
| ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(paramod_ordered,[status(thm)],[980,462]) ).
thf(999,plain,
( ( ( sk9 @ sk6 @ ( sk9 @ p ) )
!= ( sk9 @ sk6 @ ( sk9 @ p ) ) )
| ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[998]) ).
thf(1000,plain,
( ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[999:[]]) ).
thf(11,plain,
! [A: '$world'] :
( ( sk8 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(28,plain,
! [A: '$world'] :
( ( sk8 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[11]) ).
thf(1044,plain,
! [A: '$world'] :
( ( ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( sk8 @ ( A @ p ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[1000,28]) ).
thf(1045,plain,
! [A: '$world'] :
( ( ( sk8 @ sk7 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( sk8 @ ( A @ p ) )
| sk1 ),
inference(simp,[status(thm)],[1044]) ).
thf(1046,plain,
( ( sk8 @ ( sk8 @ sk7 @ p ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[1045:[bind(A,$thf( sk8 @ sk7 ))]]) ).
thf(7,plain,
! [B: $i,A: '$world'] :
( ~ ( B @ ( B @ sk7 @ p ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(26,plain,
! [B: $i,A: '$world'] :
( ~ ( B @ ( B @ sk7 @ p ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[7]) ).
thf(1191,plain,
! [B: $i,A: '$world'] :
( ( ( sk8 @ ( sk8 @ sk7 @ p ) )
!= ( B @ ( B @ sk7 @ p ) ) )
| ~ $true
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[1046,26]) ).
thf(1192,plain,
! [B: $i,A: '$world'] :
( ( ( sk8 @ ( sk8 @ sk7 @ p ) )
!= ( B @ ( B @ sk7 @ p ) ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[1191]) ).
thf(1193,plain,
! [A: '$world'] :
( ~ ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[1192:[bind(A,$thf( A )),bind(B,$thf( sk8 ))]]) ).
thf(18,plain,
( ~ sk1
| ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
( ~ sk1
| ( sk4 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(20,plain,
! [B: '$world',A: $i] :
( ~ sk1
| ( B @ sk3 @ ( B @ p ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(506,plain,
! [B: '$world',A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$accessible_world' ) )
!= ( B @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| ( B @ sk3 @ ( B @ p ) )
| ~ $true
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[9,20]) ).
thf(507,plain,
! [B: '$world',A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$accessible_world' ) )
!= ( B @ ( '$local_world' @ '$accessible_world' ) ) )
| ( B @ sk3 @ ( B @ p ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[506]) ).
thf(508,plain,
! [A: $i] :
( ( sk4 @ sk3 @ ( sk4 @ p ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[507:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(5184,plain,
! [A: $i] :
( ( ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( sk4 @ sk3 @ ( sk4 @ p ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[18,508]) ).
thf(5185,plain,
! [A: $i] :
( ( ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( sk4 @ sk3 @ ( sk4 @ p ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[5184]) ).
thf(5186,plain,
( ( sk4 @ sk3 @ ( sk4 @ p ) )
| ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[5185:[bind(A,$thf( sk5 ))]]) ).
thf(19,plain,
! [B: '$world',A: $i] :
( ~ sk1
| ( B @ sk3 @ ( B @ '$exists_in_world_$i' ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(335,plain,
! [B: '$world',A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$accessible_world' ) )
!= ( B @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| ( B @ sk3 @ ( B @ '$exists_in_world_$i' ) )
| ~ $true
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[9,19]) ).
thf(336,plain,
! [B: '$world',A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$accessible_world' ) )
!= ( B @ ( '$local_world' @ '$accessible_world' ) ) )
| ( B @ sk3 @ ( B @ '$exists_in_world_$i' ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[335]) ).
thf(337,plain,
! [A: $i] :
( ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[336:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(2557,plain,
! [A: $i] :
( ( ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[18,337]) ).
thf(2558,plain,
! [A: $i] :
( ( ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ( A @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[2557]) ).
thf(2559,plain,
( ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[2558:[bind(A,$thf( sk5 ))]]) ).
thf(10,plain,
! [A: $i] :
( ~ sk1
| ~ ( A @ ( sk4 @ p ) )
| ~ ( A @ ( sk4 @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(22,plain,
! [A: $i] :
( ~ sk1
| ~ ( A @ ( sk4 @ p ) )
| ~ ( A @ ( sk4 @ '$exists_in_world_$i' ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(2674,plain,
! [A: $i] :
( ( ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
!= ( A @ ( sk4 @ '$exists_in_world_$i' ) ) )
| ~ sk1
| ~ ( A @ ( sk4 @ p ) )
| ~ $true
| ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[2559,22]) ).
thf(2675,plain,
! [A: $i] :
( ( ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
!= ( A @ ( sk4 @ '$exists_in_world_$i' ) ) )
| ~ ( A @ ( sk4 @ p ) )
| ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[2674]) ).
thf(2676,plain,
( ~ ( sk4 @ sk3 @ ( sk4 @ p ) )
| ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[2675:[bind(A,$thf( sk4 @ sk3 ))]]) ).
thf(5238,plain,
( ( ( sk4 @ sk3 @ ( sk4 @ p ) )
!= ( sk4 @ sk3 @ ( sk4 @ p ) ) )
| ~ $true
| ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1
| ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[5186,2676]) ).
thf(5239,plain,
( ( ( sk4 @ sk3 @ ( sk4 @ p ) )
!= ( sk4 @ sk3 @ ( sk4 @ p ) ) )
| ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[5238]) ).
thf(5240,plain,
( ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[5239:[]]) ).
thf(13,plain,
! [A: '$world'] :
( ~ sk1
| ( sk5 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(23,plain,
! [A: '$world'] :
( ~ sk1
| ( sk5 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
! [B: '$world',A: $i] :
( ~ sk1
| ( B @ sk3 @ ( B @ '$exists_in_world_$i' ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(148,plain,
! [B: '$world',A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$accessible_world' ) )
!= ( B @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| ( B @ sk3 @ ( B @ '$exists_in_world_$i' ) )
| ~ $true
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[9,15]) ).
thf(149,plain,
! [B: '$world',A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$accessible_world' ) )
!= ( B @ ( '$local_world' @ '$accessible_world' ) ) )
| ( B @ sk3 @ ( B @ '$exists_in_world_$i' ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [A: $i] :
( ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(3228,plain,
! [A: $i] :
( ( ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[18,150]) ).
thf(3229,plain,
! [A: $i] :
( ( ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ sk1 ),
inference(simp,[status(thm)],[3228]) ).
thf(3230,plain,
( ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ~ ( sk5 @ ( sk5 @ sk2 @ p ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[3229:[bind(A,$thf( sk5 ))]]) ).
thf(14,plain,
! [B: '$world',A: $i] :
( ~ sk1
| ( B @ sk3 @ ( B @ p ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(62,plain,
! [B: '$world',A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$accessible_world' ) )
!= ( B @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| ( B @ sk3 @ ( B @ p ) )
| ~ $true
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[9,14]) ).
thf(63,plain,
! [B: '$world',A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$accessible_world' ) )
!= ( B @ ( '$local_world' @ '$accessible_world' ) ) )
| ( B @ sk3 @ ( B @ p ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
! [A: $i] :
( ( sk4 @ sk3 @ ( sk4 @ p ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(1303,plain,
! [A: $i] :
( ( ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( sk4 @ sk3 @ ( sk4 @ p ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[18,64]) ).
thf(1304,plain,
! [A: $i] :
( ( ( sk5 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( sk4 @ sk3 @ ( sk4 @ p ) )
| ~ ( A @ ( A @ sk2 @ p ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1303]) ).
thf(1305,plain,
( ( sk4 @ sk3 @ ( sk4 @ p ) )
| ~ ( sk5 @ ( sk5 @ sk2 @ p ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[1304:[bind(A,$thf( sk5 ))]]) ).
thf(1370,plain,
! [A: '$world'] :
( ( ( sk5 @ ( A @ p ) )
!= ( sk5 @ ( sk5 @ sk2 @ p ) ) )
| ( sk4 @ sk3 @ ( sk4 @ p ) )
| ~ $true
| ~ sk1
| ~ sk1
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(paramod_ordered,[status(thm)],[23,1305]) ).
thf(1371,plain,
! [A: '$world'] :
( ( ( sk5 @ ( A @ p ) )
!= ( sk5 @ ( sk5 @ sk2 @ p ) ) )
| ( sk4 @ sk3 @ ( sk4 @ p ) )
| ~ sk1
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[1370]) ).
thf(1372,plain,
( ( sk4 @ sk3 @ ( sk4 @ p ) )
| ~ sk1
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(pattern_uni,[status(thm)],[1371:[bind(A,$thf( sk5 @ sk2 ))]]) ).
thf(1587,plain,
! [A: $i] :
( ( ( sk4 @ sk3 @ ( sk4 @ p ) )
!= ( A @ ( sk4 @ p ) ) )
| ~ sk1
| ~ $true
| ~ ( A @ ( sk4 @ '$exists_in_world_$i' ) )
| ~ sk1
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(paramod_ordered,[status(thm)],[1372,22]) ).
thf(1588,plain,
! [A: $i] :
( ( ( sk4 @ sk3 @ ( sk4 @ p ) )
!= ( A @ ( sk4 @ p ) ) )
| ~ ( A @ ( sk4 @ '$exists_in_world_$i' ) )
| ~ sk1
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[1587]) ).
thf(1589,plain,
( ~ ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
| ~ sk1
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(pattern_uni,[status(thm)],[1588:[bind(A,$thf( sk4 @ sk3 ))]]) ).
thf(3379,plain,
( ( ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
!= ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) ) )
| ~ $true
| ~ sk1
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( sk5 @ ( sk5 @ sk2 @ p ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[3230,1589]) ).
thf(3380,plain,
( ( ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) )
!= ( sk4 @ sk3 @ ( sk4 @ '$exists_in_world_$i' ) ) )
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( sk5 @ ( sk5 @ sk2 @ p ) )
| ~ sk1 ),
inference(simp,[status(thm)],[3379]) ).
thf(3381,plain,
( ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( sk5 @ ( sk5 @ sk2 @ p ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[3380:[]]) ).
thf(3798,plain,
! [A: '$world'] :
( ( ( sk5 @ ( A @ p ) )
!= ( sk5 @ ( sk5 @ sk2 @ p ) ) )
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ $true
| ~ sk1
| ~ sk1
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(paramod_ordered,[status(thm)],[23,3381]) ).
thf(3799,plain,
! [A: '$world'] :
( ( ( sk5 @ ( A @ p ) )
!= ( sk5 @ ( sk5 @ sk2 @ p ) ) )
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[3798]) ).
thf(3800,plain,
( ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(pattern_uni,[status(thm)],[3799:[bind(A,$thf( sk5 @ sk2 ))]]) ).
thf(3815,plain,
( ~ sk1
| ~ ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[3800]) ).
thf(5332,plain,
( ( ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
!= ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[5240,3815]) ).
thf(5333,plain,
( ( ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) )
!= ( sk5 @ sk2 @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[5332]) ).
thf(5334,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[5333:[]]) ).
thf(5423,plain,
( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| $false ),
inference(rewrite,[status(thm)],[21,5334]) ).
thf(5424,plain,
sk8 @ ( '$local_world' @ '$exists_in_world_$i' ),
inference(simp,[status(thm)],[5423]) ).
thf(5844,plain,
! [A: '$world'] :
( ~ $true
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| $false ),
inference(rewrite,[status(thm)],[1193,5424,5334]) ).
thf(5845,plain,
! [A: '$world'] :
( ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[5844]) ).
thf(5417,plain,
( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| $false ),
inference(rewrite,[status(thm)],[6,5334]) ).
thf(5418,plain,
sk9 @ ( '$local_world' @ '$accessible_world' ),
inference(simp,[status(thm)],[5417]) ).
thf(8,plain,
! [B: $i,A: '$world'] :
( ~ ( B @ ( B @ sk7 @ p ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(29,plain,
! [B: $i,A: '$world'] :
( ~ ( B @ ( B @ sk7 @ p ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[8]) ).
thf(1186,plain,
! [B: $i,A: '$world'] :
( ( ( sk8 @ ( sk8 @ sk7 @ p ) )
!= ( B @ ( B @ sk7 @ p ) ) )
| ~ $true
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[1046,29]) ).
thf(1187,plain,
! [B: $i,A: '$world'] :
( ( ( sk8 @ ( sk8 @ sk7 @ p ) )
!= ( B @ ( B @ sk7 @ p ) ) )
| ~ ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[1186]) ).
thf(1188,plain,
! [A: '$world'] :
( ~ ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[1187:[bind(A,$thf( A )),bind(B,$thf( sk8 ))]]) ).
thf(5732,plain,
! [A: '$world'] :
( ~ $true
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| $false ),
inference(rewrite,[status(thm)],[1188,5424,5334]) ).
thf(5733,plain,
! [A: '$world'] :
( ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[5732]) ).
thf(5745,plain,
! [A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( A @ sk6 @ ( A @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5418,5733]) ).
thf(5746,plain,
! [A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( A @ sk6 @ ( A @ p ) ) ),
inference(simp,[status(thm)],[5745]) ).
thf(5747,plain,
sk9 @ sk6 @ ( sk9 @ p ),
inference(pattern_uni,[status(thm)],[5746:[bind(A,$thf( sk9 ))]]) ).
thf(5403,plain,
! [A: $i] :
( ~ ( A @ ( sk9 @ p ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) )
| $false ),
inference(rewrite,[status(thm)],[24,5334]) ).
thf(5404,plain,
! [A: $i] :
( ~ ( A @ ( sk9 @ p ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) ) ),
inference(simp,[status(thm)],[5403]) ).
thf(5756,plain,
! [A: $i] :
( ( ( sk9 @ sk6 @ ( sk9 @ p ) )
!= ( A @ ( sk9 @ p ) ) )
| ~ $true
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) ) ),
inference(paramod_ordered,[status(thm)],[5747,5404]) ).
thf(5757,plain,
! [A: $i] :
( ( ( sk9 @ sk6 @ ( sk9 @ p ) )
!= ( A @ ( sk9 @ p ) ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) ) ),
inference(simp,[status(thm)],[5756]) ).
thf(5758,plain,
~ ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) ),
inference(pattern_uni,[status(thm)],[5757:[bind(A,$thf( sk9 @ sk6 ))]]) ).
thf(5857,plain,
! [A: '$world'] :
( ( ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
!= ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) ) )
| ~ $true
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(paramod_ordered,[status(thm)],[5845,5758]) ).
thf(5858,plain,
! [A: '$world'] :
( ( ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
!= ( sk9 @ sk6 @ ( sk9 @ '$exists_in_world_$i' ) ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[5857]) ).
thf(5859,plain,
~ ( sk9 @ ( '$local_world' @ '$accessible_world' ) ),
inference(pattern_uni,[status(thm)],[5858:[bind(A,$thf( sk9 ))]]) ).
thf(5876,plain,
~ $true,
inference(rewrite,[status(thm)],[5859,5418]) ).
thf(5877,plain,
$false,
inference(simp,[status(thm)],[5876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO955_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % 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
% 0.17/0.41 % Computer : n015.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Sat Sep 26 20:23:15 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 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
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.15 % [INFO] Parsing done (167ms).
% 1.19/1.17 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.19/1.19 %%% First-order logic specification detected, trying modal-logic-to-TXF embedding (redirected from embedding '$$modal' to embedding '$$fomlModel' version 1.3.7) ... Use flag -p FORCE_HIGHERORDER if you want to have THF output instead.
% 1.30/1.29 % [INFO] Running in sequential loop mode.
% 1.84/1.67 % [INFO] eprover registered as external prover.
% 1.84/1.68 % [INFO] Scanning for conjecture ...
% 2.03/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.18/1.81 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.18/1.82 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.18/1.82 % [INFO] Type checking passed.
% 2.18/1.82 % [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 ...
% 20.42/5.49 % [INFO] Killing All external provers ...
% 20.42/5.50 % Time passed: 4933ms (effective reasoning time: 4192ms)
% 20.42/5.50 % 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)>
% 20.42/5.50 % Axioms used in derivation (0):
% 20.42/5.50 % No. of inferences in proof: 124
% 15.77/5.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4933 ms resp. 4192 ms w/o parsing
% 15.77/5.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.77/5.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------