%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO956_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.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 7.80s 3.60s
% Output : Refutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 9
% Syntax : Number of formulae : 105 ( 16 unt; 0 typ; 8 def)
% Number of atoms : 515 ( 44 equ; 0 cnn)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 1151 ( 228 ~; 258 |; 38 &; 593 @)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 107 ( 4 ^; 77 !; 18 ?; 107 :)
% ( 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: $o ).
thf(sk3_decl,type,
sk3: '$world' ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > '$world' ).
thf(sk6_decl,type,
sk6: '$world' > $i ).
thf(sk7_decl,type,
sk7: $o ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: '$world' ).
thf(sk10_decl,type,
sk10: '$world' > $i ).
thf(sk11_decl,type,
sk11: $i > '$world' ).
thf(sk3_def,definition,
( sk3
= ( @+[A: '$world'] :
~ ( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: '$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(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: '$world'] :
@+[B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: '$world'] :
~ ( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [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: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) )
=> ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence23) ).
thf(2,negated_conjecture,
~ ( ( ! [A: '$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: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) )
=> ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( ( ( ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) )
=> ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) )
=> ( ! [A: '$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: $i] :
( ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ) )
=> ( ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ? [B: '$world'] :
( ~ ( A @ ( B @ p ) )
& ( B @ ( '$local_world' @ '$accessible_world' ) ) ) )
=> ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ~ ( B @ ( A @ p ) ) )
& ( A @ ( '$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: $i] :
( ( ~ ( H @ ( H @ sk11 @ p ) )
| ~ ( H @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 )
& ( ( H @ sk11 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( H @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 )
& ( ( G @ sk10 @ ( G @ p ) )
| ~ ( G @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( ( G @ sk10 @ ( G @ '$exists_in_world_$i' ) )
| ~ ( G @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( ~ ( F @ ( sk9 @ p ) )
| ~ ( F @ ( sk9 @ '$exists_in_world_$i' ) )
| ~ sk7
| sk1 )
& ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk7
| sk1 )
& ( sk7
| ( sk8 @ ( E @ p ) )
| ~ ( E @ ( '$local_world' @ '$accessible_world' ) )
| sk1 )
& ( sk7
| ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 )
& ( ~ sk1
| ( D @ sk6 @ ( D @ p ) )
| ~ ( D @ ( '$local_world' @ '$accessible_world' ) ) )
& ( ~ sk1
| ( D @ sk6 @ ( D @ '$exists_in_world_$i' ) )
| ~ ( D @ ( '$local_world' @ '$accessible_world' ) ) )
& ( ~ sk1
| ~ ( C @ ( C @ sk5 @ p ) )
| ~ ( C @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
& ( ~ sk1
| ( C @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( C @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
& ( ~ sk1
| ( sk4 @ ( B @ p ) )
| ~ ( B @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk2 )
& ( ~ sk1
| ( sk4 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk2 )
& ( ~ sk1
| sk2
| ~ ( A @ ( sk3 @ p ) )
| ~ ( A @ ( sk3 @ '$exists_in_world_$i' ) ) )
& ( ~ sk1
| sk2
| ( sk3 @ ( '$local_world' @ '$accessible_world' ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(21,plain,
( sk7
| ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [A: $i] :
( ( A @ sk11 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(22,plain,
! [A: $i] :
( ( A @ sk11 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 ),
inference(simp,[status(thm)],[10]) ).
thf(51,plain,
! [A: $i] :
( ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( A @ sk11 @ ( '$local_world' @ '$accessible_world' ) )
| ~ $true
| sk1
| sk7
| sk1 ),
inference(paramod_ordered,[status(thm)],[21,22]) ).
thf(52,plain,
! [A: $i] :
( ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( A @ sk11 @ ( '$local_world' @ '$accessible_world' ) )
| sk7
| sk1 ),
inference(simp,[status(thm)],[51]) ).
thf(53,plain,
( ( sk8 @ sk11 @ ( '$local_world' @ '$accessible_world' ) )
| sk7
| sk1 ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( sk8 ))]]) ).
thf(20,plain,
! [A: '$world'] :
( sk7
| ( sk8 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(24,plain,
! [A: '$world'] :
( sk7
| ( sk8 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[20]) ).
thf(107,plain,
! [A: '$world'] :
( ( ( sk8 @ sk11 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| sk7
| ( sk8 @ ( A @ p ) )
| ~ $true
| sk1
| sk7
| sk1 ),
inference(paramod_ordered,[status(thm)],[53,24]) ).
thf(108,plain,
! [A: '$world'] :
( ( ( sk8 @ sk11 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( sk8 @ ( A @ p ) )
| sk7
| sk1 ),
inference(simp,[status(thm)],[107]) ).
thf(109,plain,
( ( sk8 @ ( sk8 @ sk11 @ p ) )
| sk7
| sk1 ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( sk8 @ sk11 ))]]) ).
thf(6,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk11 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(25,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk11 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1 ),
inference(simp,[status(thm)],[6]) ).
thf(210,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ sk11 @ p ) )
!= ( A @ ( A @ sk11 @ p ) ) )
| ~ $true
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk1
| sk7
| sk1 ),
inference(paramod_ordered,[status(thm)],[109,25]) ).
thf(211,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ sk11 @ p ) )
!= ( A @ ( A @ sk11 @ p ) ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk7
| sk1 ),
inference(simp,[status(thm)],[210]) ).
thf(212,plain,
( ~ ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| sk7
| sk1 ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( sk8 ))]]) ).
thf(258,plain,
( ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ~ $true
| sk7
| sk1
| sk7
| sk1 ),
inference(paramod_ordered,[status(thm)],[21,212]) ).
thf(259,plain,
( ( ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( sk8 @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| sk7
| sk1 ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
( sk7
| sk1 ),
inference(pattern_uni,[status(thm)],[259:[]]) ).
thf(12,plain,
( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk7
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(265,plain,
( ( sk7 != sk7 )
| ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[260,12]) ).
thf(266,plain,
( ( sk7 != sk7 )
| ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[265]) ).
thf(267,plain,
( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[266:[]]) ).
thf(18,plain,
( ~ sk1
| sk2
| ( sk3 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(11,plain,
! [A: '$world'] :
( ~ sk1
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(30,plain,
! [A: '$world'] :
( ~ sk1
| ( A @ sk6 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(17,plain,
! [A: '$world'] :
( ~ sk1
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(27,plain,
! [A: '$world'] :
( ~ sk1
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(307,plain,
! [A: '$world'] :
( ( ( sk3 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ $true
| ~ sk1
| sk2 ),
inference(paramod_ordered,[status(thm)],[18,27]) ).
thf(308,plain,
! [A: '$world'] :
( ( ( sk3 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( A @ sk6 @ ( A @ '$exists_in_world_$i' ) )
| ~ sk1
| sk2 ),
inference(simp,[status(thm)],[307]) ).
thf(309,plain,
( ( sk3 @ sk6 @ ( sk3 @ '$exists_in_world_$i' ) )
| ~ sk1
| sk2 ),
inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( sk3 ))]]) ).
thf(13,plain,
! [A: $i] :
( ~ sk1
| sk2
| ~ ( A @ ( sk3 @ p ) )
| ~ ( A @ ( sk3 @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(369,plain,
! [A: $i] :
( ( ( sk3 @ sk6 @ ( sk3 @ '$exists_in_world_$i' ) )
!= ( A @ ( sk3 @ '$exists_in_world_$i' ) ) )
| ~ sk1
| sk2
| ~ ( A @ ( sk3 @ p ) )
| ~ $true
| ~ sk1
| sk2 ),
inference(paramod_ordered,[status(thm)],[309,13]) ).
thf(370,plain,
! [A: $i] :
( ( ( sk3 @ sk6 @ ( sk3 @ '$exists_in_world_$i' ) )
!= ( A @ ( sk3 @ '$exists_in_world_$i' ) ) )
| ~ ( A @ ( sk3 @ p ) )
| ~ sk1
| sk2 ),
inference(simp,[status(thm)],[369]) ).
thf(371,plain,
( ~ ( sk3 @ sk6 @ ( sk3 @ p ) )
| ~ sk1
| sk2 ),
inference(pattern_uni,[status(thm)],[370:[bind(A,$thf( sk3 @ sk6 ))]]) ).
thf(407,plain,
! [A: '$world'] :
( ( ( A @ sk6 @ ( A @ p ) )
!= ( sk3 @ sk6 @ ( sk3 @ p ) ) )
| ~ $true
| ~ sk1
| sk2
| ~ sk1
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(paramod_ordered,[status(thm)],[30,371]) ).
thf(408,plain,
! [A: '$world'] :
( ( ( A @ sk6 @ ( A @ p ) )
!= ( sk3 @ sk6 @ ( sk3 @ p ) ) )
| sk2
| ~ sk1
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[407]) ).
thf(409,plain,
( sk2
| ~ sk1
| ~ ( sk3 @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( sk3 ))]]) ).
thf(464,plain,
( ( ( sk3 @ ( '$local_world' @ '$accessible_world' ) )
!= ( sk3 @ ( '$local_world' @ '$accessible_world' ) ) )
| sk2
| ~ sk1
| ~ $true
| ~ sk1
| sk2 ),
inference(paramod_ordered,[status(thm)],[18,409]) ).
thf(465,plain,
( ( ( sk3 @ ( '$local_world' @ '$accessible_world' ) )
!= ( sk3 @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| sk2 ),
inference(simp,[status(thm)],[464]) ).
thf(466,plain,
( ~ sk1
| sk2 ),
inference(pattern_uni,[status(thm)],[465:[]]) ).
thf(19,plain,
( ~ sk1
| ( sk4 @ ( '$local_world' @ '$exists_in_world_$i' ) )
| ~ sk2 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(7,plain,
! [A: $i] :
( ~ sk1
| ( A @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(28,plain,
! [A: $i] :
( ~ sk1
| ( A @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(63,plain,
! [A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ~ sk1
| ( A @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
| ~ $true
| ~ sk1
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[19,28]) ).
thf(64,plain,
! [A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ( A @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1
| ~ sk2 ),
inference(simp,[status(thm)],[63]) ).
thf(65,plain,
( ( sk4 @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk1
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( sk4 ))]]) ).
thf(9,plain,
! [A: '$world'] :
( ~ sk1
| ( sk4 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk2 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(26,plain,
! [A: '$world'] :
( ~ sk1
| ( sk4 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk2 ),
inference(simp,[status(thm)],[9]) ).
thf(16,plain,
! [A: $i] :
( ~ sk1
| ~ ( A @ ( A @ sk5 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(29,plain,
! [A: $i] :
( ~ sk1
| ~ ( A @ ( A @ sk5 @ p ) )
| ~ ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(38,plain,
! [A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ~ sk1
| ~ ( A @ ( A @ sk5 @ p ) )
| ~ $true
| ~ sk1
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[19,29]) ).
thf(39,plain,
! [A: $i] :
( ( ( sk4 @ ( '$local_world' @ '$exists_in_world_$i' ) )
!= ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
| ~ ( A @ ( A @ sk5 @ p ) )
| ~ sk1
| ~ sk2 ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
( ~ ( sk4 @ ( sk4 @ sk5 @ p ) )
| ~ sk1
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( sk4 ))]]) ).
thf(91,plain,
! [A: '$world'] :
( ( ( sk4 @ ( A @ p ) )
!= ( sk4 @ ( sk4 @ sk5 @ p ) ) )
| ~ $true
| ~ sk1
| ~ sk2
| ~ sk1
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[26,40]) ).
thf(92,plain,
! [A: '$world'] :
( ( ( sk4 @ ( A @ p ) )
!= ( sk4 @ ( sk4 @ sk5 @ p ) ) )
| ~ sk1
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk2 ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
( ~ sk1
| ~ ( sk4 @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk4 @ sk5 ))]]) ).
thf(141,plain,
( ( ( sk4 @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
!= ( sk4 @ sk5 @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| ~ $true
| ~ sk2
| ~ sk1
| ~ sk2 ),
inference(paramod_ordered,[status(thm)],[65,93]) ).
thf(142,plain,
( ( ( sk4 @ sk5 @ ( '$local_world' @ '$accessible_world' ) )
!= ( sk4 @ sk5 @ ( '$local_world' @ '$accessible_world' ) ) )
| ~ sk1
| ~ sk2 ),
inference(simp,[status(thm)],[141]) ).
thf(143,plain,
( ~ sk1
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[142:[]]) ).
thf(471,plain,
( ( sk2 != sk2 )
| ~ sk1
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[466,143]) ).
thf(472,plain,
( ( sk2 != sk2 )
| ~ sk1 ),
inference(simp,[status(thm)],[471]) ).
thf(473,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[472:[]]) ).
thf(494,plain,
( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
| $false ),
inference(rewrite,[status(thm)],[267,473]) ).
thf(495,plain,
sk9 @ ( '$local_world' @ '$accessible_world' ),
inference(simp,[status(thm)],[494]) ).
thf(8,plain,
! [A: '$world'] :
( ( A @ sk10 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(31,plain,
! [A: '$world'] :
( ( A @ sk10 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[8]) ).
thf(496,plain,
! [A: '$world'] :
( ( A @ sk10 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| $false ),
inference(rewrite,[status(thm)],[31,473]) ).
thf(497,plain,
! [A: '$world'] :
( ( A @ sk10 @ ( A @ '$exists_in_world_$i' ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) ) ),
inference(simp,[status(thm)],[496]) ).
thf(498,plain,
! [A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( A @ sk10 @ ( A @ '$exists_in_world_$i' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[495,497]) ).
thf(499,plain,
! [A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( A @ sk10 @ ( A @ '$exists_in_world_$i' ) ) ),
inference(simp,[status(thm)],[498]) ).
thf(500,plain,
sk9 @ sk10 @ ( sk9 @ '$exists_in_world_$i' ),
inference(pattern_uni,[status(thm)],[499:[bind(A,$thf( sk9 ))]]) ).
thf(15,plain,
! [A: $i] :
( ~ ( A @ ( sk9 @ p ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) )
| ~ sk7
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(32,plain,
! [A: $i] :
( ~ ( A @ ( sk9 @ p ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) )
| ~ sk7
| sk1 ),
inference(simp,[status(thm)],[15]) ).
thf(480,plain,
( sk7
| $false ),
inference(rewrite,[status(thm)],[260,473]) ).
thf(481,plain,
sk7,
inference(simp,[status(thm)],[480]) ).
thf(530,plain,
! [A: $i] :
( ~ ( A @ ( sk9 @ p ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) )
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[32,481,473]) ).
thf(531,plain,
! [A: $i] :
( ~ ( A @ ( sk9 @ p ) )
| ~ ( A @ ( sk9 @ '$exists_in_world_$i' ) ) ),
inference(simp,[status(thm)],[530]) ).
thf(532,plain,
! [A: $i] :
( ( ( sk9 @ sk10 @ ( sk9 @ '$exists_in_world_$i' ) )
!= ( A @ ( sk9 @ '$exists_in_world_$i' ) ) )
| ~ ( A @ ( sk9 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[500,531]) ).
thf(533,plain,
! [A: $i] :
( ( ( sk9 @ sk10 @ ( sk9 @ '$exists_in_world_$i' ) )
!= ( A @ ( sk9 @ '$exists_in_world_$i' ) ) )
| ~ ( A @ ( sk9 @ p ) ) ),
inference(simp,[status(thm)],[532]) ).
thf(534,plain,
~ ( sk9 @ sk10 @ ( sk9 @ p ) ),
inference(pattern_uni,[status(thm)],[533:[bind(A,$thf( sk9 @ sk10 ))]]) ).
thf(14,plain,
! [A: '$world'] :
( ( A @ sk10 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(23,plain,
! [A: '$world'] :
( ( A @ sk10 @ ( A @ p ) )
| ~ ( A @ ( '$local_world' @ '$accessible_world' ) )
| sk1 ),
inference(simp,[status(thm)],[14]) ).
thf(159,plain,
! [A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( A @ sk10 @ ( A @ p ) )
| ~ $true
| sk1
| ~ sk7
| sk1 ),
inference(paramod_ordered,[status(thm)],[12,23]) ).
thf(160,plain,
! [A: '$world'] :
( ( ( sk9 @ ( '$local_world' @ '$accessible_world' ) )
!= ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ( A @ sk10 @ ( A @ p ) )
| ~ sk7
| sk1 ),
inference(simp,[status(thm)],[159]) ).
thf(161,plain,
( ( sk9 @ sk10 @ ( sk9 @ p ) )
| ~ sk7
| sk1 ),
inference(pattern_uni,[status(thm)],[160:[bind(A,$thf( sk9 ))]]) ).
thf(268,plain,
( ( sk7 != sk7 )
| ( sk9 @ sk10 @ ( sk9 @ p ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[260,161]) ).
thf(269,plain,
( ( sk7 != sk7 )
| ( sk9 @ sk10 @ ( sk9 @ p ) )
| sk1 ),
inference(simp,[status(thm)],[268]) ).
thf(270,plain,
( ( sk9 @ sk10 @ ( sk9 @ p ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[269:[]]) ).
thf(478,plain,
( ( sk9 @ sk10 @ ( sk9 @ p ) )
| $false ),
inference(rewrite,[status(thm)],[270,473]) ).
thf(479,plain,
sk9 @ sk10 @ ( sk9 @ p ),
inference(simp,[status(thm)],[478]) ).
thf(552,plain,
~ $true,
inference(rewrite,[status(thm)],[534,479]) ).
thf(553,plain,
$false,
inference(simp,[status(thm)],[552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO956_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.52 % Computer : n009.cluster.edu
% 0.13/0.52 % Model : x86_64 x86_64
% 0.13/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.52 % Memory : 8046.5625MB
% 0.13/0.52 % OS : Linux 6.8.0-71-generic
% 0.13/0.52 % CPULimit : 300
% 0.13/0.52 % WCLimit : 300
% 0.13/0.52 % DateTime : Sat Sep 26 20:19:47 UTC 2026
% 0.13/0.52 % CPUTime :
% 0.13/0.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/1.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.29 % [INFO] Parsing done (183ms).
% 1.35/1.31 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.35/1.32 %%% 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.
% 1.51/1.44 % [INFO] Running in sequential loop mode.
% 2.15/1.82 % [INFO] eprover registered as external prover.
% 2.15/1.83 % [INFO] Scanning for conjecture ...
% 2.32/1.92 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.32/1.97 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.32/1.98 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.32/1.98 % [INFO] Type checking passed.
% 2.32/1.99 % [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 ...
% 7.80/3.59 % [INFO] Killing All external provers ...
% 7.80/3.59 % Time passed: 2932ms (effective reasoning time: 2148ms)
% 7.80/3.59 % 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)>
% 7.80/3.60 % Axioms used in derivation (0):
% 7.80/3.60 % No. of inferences in proof: 97
% 7.80/3.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2932 ms resp. 2148 ms w/o parsing
% 7.32/3.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.32/3.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------