%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN550+1 : TPTP v9.3.1. Released v2.2.0.
% 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 : n007.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 09:17:49 AM UTC 2026
% Result : Theorem 13.01s 3.62s
% Output : Refutation 11.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 113 ( 10 unt; 0 typ; 6 def)
% Number of atoms : 523 ( 85 equ; 0 cnn)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 1264 ( 258 ~; 253 |; 29 &; 698 @)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 139 ( 5 ^; 114 !; 14 ?; 139 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(reachable_decl,type,
reachable: $i > $i > $o ).
thf(initial_world_decl,type,
initial_world: $i ).
thf(p_decl,type,
p: $i > $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( B @ p ) )
& ( A @ ( initial_world @ reachable ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ( A @ reachable ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ p ) )
& ( C @ ( B @ reachable ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C @ ( A @ reachable ) )
=> ( C @ p ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ p ) )
& ( C @ ( B @ reachable ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
( ! [C: $i] :
( ( C @ ( B @ reachable ) )
=> ( C @ p ) )
& ( B @ ( A @ reachable ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ ( A @ reachable ) )
=> ( B @ p ) ) ) ) ).
thf(1,conjecture,
( ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( B @ p ) )
& ( A @ ( initial_world @ reachable ) ) )
<=> ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ p ) )
& ( C @ ( B @ reachable ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
~ ( ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( B @ p ) )
& ( A @ ( initial_world @ reachable ) ) )
<=> ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ p ) )
& ( C @ ( B @ reachable ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( ( ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ p ) )
& ( C @ ( B @ reachable ) ) ) )
& ( A @ ( initial_world @ reachable ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( B @ p ) )
& ( A @ ( initial_world @ reachable ) ) ) )
& ( ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( B @ p ) )
& ( A @ ( initial_world @ reachable ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( D @ ( C @ reachable ) )
=> ( D @ p ) )
& ( C @ ( B @ reachable ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( F @ sk7 @ p )
| ~ ( F @ ( initial_world @ reachable ) )
| sk1 )
& ( ( F @ sk7 @ ( F @ reachable ) )
| ~ ( F @ ( initial_world @ reachable ) )
| sk1 )
& ( ( E @ p )
| ~ ( E @ ( D @ sk6 @ reachable ) )
| ~ ( D @ ( sk5 @ reachable ) )
| sk1 )
& ( ( D @ sk6 @ ( D @ reachable ) )
| ~ ( D @ ( sk5 @ reachable ) )
| sk1 )
& ( ( sk5 @ ( initial_world @ reachable ) )
| sk1 )
& ( ~ sk1
| ~ ( B @ ( C @ sk4 ) @ p )
| ~ ( C @ ( B @ sk3 @ reachable ) )
| ~ ( B @ ( initial_world @ reachable ) ) )
& ( ~ sk1
| ( B @ ( C @ sk4 ) @ ( C @ reachable ) )
| ~ ( C @ ( B @ sk3 @ reachable ) )
| ~ ( B @ ( initial_world @ reachable ) ) )
& ( ~ sk1
| ( B @ sk3 @ ( B @ reachable ) )
| ~ ( B @ ( initial_world @ reachable ) ) )
& ( ~ sk1
| ( A @ p )
| ~ ( A @ ( sk2 @ reachable ) ) )
& ( ~ sk1
| ( sk2 @ ( initial_world @ reachable ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(11,plain,
( ( sk5 @ ( initial_world @ reachable ) )
| sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(9,plain,
! [A: $i] :
( ( A @ sk7 @ ( A @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) )
| sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(18,plain,
! [A: $i] :
( ( A @ sk7 @ ( A @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[9]) ).
thf(86,plain,
! [A: $i] :
( ( ( sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk7 @ ( A @ reachable ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[11,18]) ).
thf(87,plain,
! [A: $i] :
( ( ( sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk7 @ ( A @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
( ( sk5 @ sk7 @ ( sk5 @ reachable ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( sk5 ))]]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ reachable ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_reachable) ).
thf(24,plain,
! [A: $i] : ( A @ ( A @ reachable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
! [A: $i] : ( A @ ( A @ reachable ) ),
inference(cnf,[status(esa)],[24]) ).
thf(14,plain,
! [A: $i] :
( ~ sk1
| ( A @ sk3 @ ( A @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(17,plain,
! [A: $i] :
( ~ sk1
| ( A @ sk3 @ ( A @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ sk1
| ( B @ sk3 @ ( B @ reachable ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,17]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ sk1
| ( B @ sk3 @ ( B @ reachable ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(106,plain,
( ~ sk1
| ( initial_world @ sk3 @ ( initial_world @ reachable ) ) ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(10,plain,
( ~ sk1
| ( sk2 @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( A @ ( B @ sk4 ) @ p )
| ~ ( B @ ( A @ sk3 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ sk1
| ~ ( A @ ( B @ sk4 ) @ p )
| ~ ( B @ ( A @ sk3 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ sk1
| ~ ( A @ ( B @ sk4 ) @ p )
| ~ ( B @ ( A @ sk3 @ reachable ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[10,23]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ ( B @ sk4 ) @ p )
| ~ ( B @ ( A @ sk3 @ reachable ) )
| ~ sk1 ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ sk4 ) @ p )
| ~ ( A @ ( sk2 @ sk3 @ reachable ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk2 ))]]) ).
thf(57,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ sk4 ) @ p )
| ~ ( A @ ( sk2 @ sk3 @ reachable ) )
| ~ sk1 ),
inference(simp,[status(thm)],[39]) ).
thf(209,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sk3 @ reachable ) )
!= ( initial_world @ sk3 @ ( initial_world @ reachable ) ) )
| ~ ( sk2 @ ( A @ sk4 ) @ p )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[106,57]) ).
thf(210,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sk3 @ reachable ) )
!= ( initial_world @ sk3 @ ( initial_world @ reachable ) ) )
| ~ ( sk2 @ ( A @ sk4 ) @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[209]) ).
thf(226,plain,
! [A: $i] :
( ( A
!= ( initial_world @ sk3 ) )
| ( ( sk2 @ sk3 )
!= initial_world )
| ~ ( sk2 @ ( A @ sk4 ) @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[210]) ).
thf(229,plain,
( ( ( sk2 @ sk3 )
!= initial_world )
| ~ ( sk2 @ ( initial_world @ sk3 @ sk4 ) @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[226]) ).
thf(13,plain,
! [A: $i] :
( ~ sk1
| ( A @ p )
| ~ ( A @ ( sk2 @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( sk2 @ reachable ) ) )
| ~ sk1
| ( B @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( sk2 @ reachable ) ) )
| ~ sk1
| ( B @ p ) ),
inference(simp,[status(thm)],[28]) ).
thf(30,plain,
( ~ sk1
| ( sk2 @ p ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( sk2 @ sk3 @ reachable ) ) )
| ~ ( sk2 @ ( B @ sk4 ) @ p )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[25,57]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( sk2 @ sk3 @ reachable ) ) )
| ~ ( sk2 @ ( B @ sk4 ) @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
( ~ ( sk2 @ ( sk2 @ sk3 @ sk4 ) @ p )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( sk2 @ sk3 )),bind(B,$thf( sk2 @ sk3 ))]]) ).
thf(189,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) @ p )
!= ( sk2 @ p ) )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[30,66]) ).
thf(190,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) @ p )
!= ( sk2 @ p ) )
| ~ sk1 ),
inference(simp,[status(thm)],[189]) ).
thf(193,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) )
!= sk2 )
| ~ sk1 ),
inference(simp,[status(thm)],[190]) ).
thf(8,plain,
! [A: $i] :
( ( A @ sk6 @ ( A @ reachable ) )
| ~ ( A @ ( sk5 @ reachable ) )
| sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(22,plain,
! [A: $i] :
( ( A @ sk6 @ ( A @ reachable ) )
| ~ ( A @ ( sk5 @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[8]) ).
thf(221,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ sk1
| ( A @ sk3 @ ( A @ reachable ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[106,17]) ).
thf(222,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk3 @ ( A @ reachable ) )
| ~ sk1 ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
( ( initial_world @ sk3 @ sk3 @ ( initial_world @ sk3 @ reachable ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( initial_world @ sk3 ))]]) ).
thf(101,plain,
! [A: $i] :
( ( ( sk2 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ sk1
| ( A @ sk3 @ ( A @ reachable ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[10,17]) ).
thf(102,plain,
! [A: $i] :
( ( ( sk2 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk3 @ ( A @ reachable ) )
| ~ sk1 ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
( ( sk2 @ sk3 @ ( sk2 @ reachable ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( sk2 ))]]) ).
thf(164,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ reachable ) )
!= ( A @ ( sk2 @ reachable ) ) )
| ~ sk1
| ( A @ p )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[103,13]) ).
thf(165,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ reachable ) )
!= ( A @ ( sk2 @ reachable ) ) )
| ( A @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[164]) ).
thf(166,plain,
( ( sk2 @ sk3 @ p )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( sk2 @ sk3 ))]]) ).
thf(191,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) @ p )
!= ( sk2 @ sk3 @ p ) )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[166,66]) ).
thf(192,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) @ p )
!= ( sk2 @ sk3 @ p ) )
| ~ sk1 ),
inference(simp,[status(thm)],[191]) ).
thf(194,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) )
!= ( sk2 @ sk3 ) )
| ~ sk1 ),
inference(simp,[status(thm)],[192]) ).
thf(211,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ reachable ) )
!= ( initial_world @ sk3 @ ( initial_world @ reachable ) ) )
| ~ sk1
| ( A @ p )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[106,13]) ).
thf(212,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ reachable ) )
!= ( initial_world @ sk3 @ ( initial_world @ reachable ) ) )
| ( A @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[211]) ).
thf(225,plain,
! [A: $i] :
( ( A
!= ( initial_world @ sk3 ) )
| ( sk2 != initial_world )
| ~ sk1
| ( A @ p ) ),
inference(simp,[status(thm)],[212]) ).
thf(228,plain,
( ( sk2 != initial_world )
| ~ sk1
| ( initial_world @ sk3 @ p ) ),
inference(simp,[status(thm)],[225]) ).
thf(235,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) @ p )
!= ( initial_world @ sk3 @ p ) )
| ~ $true
| ~ sk1
| ( sk2 != initial_world )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[228,66]) ).
thf(236,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) @ p )
!= ( initial_world @ sk3 @ p ) )
| ( sk2 != initial_world )
| ~ sk1 ),
inference(simp,[status(thm)],[235]) ).
thf(239,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ sk4 ) )
!= ( initial_world @ sk3 ) )
| ( sk2 != initial_world )
| ~ sk1 ),
inference(simp,[status(thm)],[236]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk7 @ ( B @ reachable ) )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[25,18]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ( B @ sk7 @ ( B @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
( ( initial_world @ sk7 @ ( initial_world @ reachable ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(16,plain,
! [A: $i] :
( ~ ( A @ sk7 @ p )
| ~ ( A @ ( initial_world @ reachable ) )
| sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(21,plain,
! [A: $i] :
( ~ ( A @ sk7 @ p )
| ~ ( A @ ( initial_world @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[16]) ).
thf(438,plain,
! [A: $i] :
( ( ( initial_world @ sk7 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk7 @ p )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[76,21]) ).
thf(439,plain,
! [A: $i] :
( ( ( initial_world @ sk7 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk7 @ p )
| sk1 ),
inference(simp,[status(thm)],[438]) ).
thf(440,plain,
( ~ ( initial_world @ sk7 @ sk7 @ p )
| sk1 ),
inference(pattern_uni,[status(thm)],[439:[bind(A,$thf( initial_world @ sk7 ))]]) ).
thf(140,plain,
! [A: $i] :
( ( ( initial_world @ sk7 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk7 @ ( A @ reachable ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[76,18]) ).
thf(141,plain,
! [A: $i] :
( ( ( initial_world @ sk7 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk7 @ ( A @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[140]) ).
thf(142,plain,
( ( initial_world @ sk7 @ sk7 @ ( initial_world @ sk7 @ reachable ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( initial_world @ sk7 ))]]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( B @ p )
| ~ ( B @ ( A @ sk6 @ reachable ) )
| ~ ( A @ ( sk5 @ reachable ) )
| sk1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ p )
| ~ ( B @ ( A @ sk6 @ reachable ) )
| ~ ( A @ ( sk5 @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[7]) ).
thf(419,plain,
! [A: $i] :
( ( ( sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk7 @ p )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[11,21]) ).
thf(420,plain,
! [A: $i] :
( ( ( sk5 @ ( initial_world @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk7 @ p )
| sk1 ),
inference(simp,[status(thm)],[419]) ).
thf(421,plain,
( ~ ( sk5 @ sk7 @ p )
| sk1 ),
inference(pattern_uni,[status(thm)],[420:[bind(A,$thf( sk5 ))]]) ).
thf(62,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sk3 @ reachable ) )
!= ( sk2 @ ( initial_world @ reachable ) ) )
| ~ ( sk2 @ ( A @ sk4 ) @ p )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[10,57]) ).
thf(63,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ sk3 @ reachable ) )
!= ( sk2 @ ( initial_world @ reachable ) ) )
| ~ ( sk2 @ ( A @ sk4 ) @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[62]) ).
thf(69,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk2 @ sk3 )
!= initial_world )
| ~ ( sk2 @ ( A @ sk4 ) @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[63]) ).
thf(70,plain,
( ( ( sk2 @ sk3 )
!= initial_world )
| ~ ( sk2 @ ( sk2 @ sk4 ) @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[69]) ).
thf(154,plain,
! [A: $i] :
( ( ( sk5 @ sk7 @ ( sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk7 @ ( A @ reachable ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[88,18]) ).
thf(155,plain,
! [A: $i] :
( ( ( sk5 @ sk7 @ ( sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk7 @ ( A @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[154]) ).
thf(160,plain,
! [A: $i] :
( ( ( sk5 @ sk7 )
!= A )
| ( sk5 != initial_world )
| ( A @ sk7 @ ( A @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[155]) ).
thf(161,plain,
( ( sk5 != initial_world )
| ( sk5 @ sk7 @ sk7 @ ( sk5 @ sk7 @ reachable ) )
| sk1 ),
inference(simp,[status(thm)],[160]) ).
thf(167,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ sk1
| ( A @ sk3 @ ( A @ reachable ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[103,17]) ).
thf(168,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ( A @ sk3 @ ( A @ reachable ) )
| ~ sk1 ),
inference(simp,[status(thm)],[167]) ).
thf(177,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= A )
| ( sk2 != initial_world )
| ~ sk1
| ( A @ sk3 @ ( A @ reachable ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(180,plain,
( ( sk2 != initial_world )
| ~ sk1
| ( sk2 @ sk3 @ sk3 @ ( sk2 @ sk3 @ reachable ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(371,plain,
( ( ( sk2 @ ( sk2 @ sk4 ) @ p )
!= ( sk2 @ p ) )
| ( ( sk2 @ sk3 )
!= initial_world )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[30,70]) ).
thf(372,plain,
( ( ( sk2 @ ( sk2 @ sk4 ) @ p )
!= ( sk2 @ p ) )
| ( ( sk2 @ sk3 )
!= initial_world )
| ~ sk1 ),
inference(simp,[status(thm)],[371]) ).
thf(375,plain,
( ( ( sk2 @ ( sk2 @ sk4 ) )
!= sk2 )
| ( ( sk2 @ sk3 )
!= initial_world )
| ~ sk1 ),
inference(simp,[status(thm)],[372]) ).
thf(339,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ sk3 @ ( initial_world @ sk3 @ reachable ) )
!= ( A @ ( sk2 @ reachable ) ) )
| ~ sk1
| ( A @ p )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[223,13]) ).
thf(340,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ sk3 @ ( initial_world @ sk3 @ reachable ) )
!= ( A @ ( sk2 @ reachable ) ) )
| ( A @ p )
| ~ sk1 ),
inference(simp,[status(thm)],[339]) ).
thf(357,plain,
! [A: $i] :
( ( ( initial_world @ sk3 @ sk3 )
!= A )
| ( ( initial_world @ sk3 )
!= sk2 )
| ~ sk1
| ( A @ p ) ),
inference(simp,[status(thm)],[340]) ).
thf(362,plain,
( ( ( initial_world @ sk3 )
!= sk2 )
| ~ sk1
| ( initial_world @ sk3 @ sk3 @ p ) ),
inference(simp,[status(thm)],[357]) ).
thf(406,plain,
! [A: $i] :
( ( ( sk5 @ sk7 @ ( sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk7 @ p )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[88,21]) ).
thf(407,plain,
! [A: $i] :
( ( ( sk5 @ sk7 @ ( sk5 @ reachable ) )
!= ( A @ ( initial_world @ reachable ) ) )
| ~ ( A @ sk7 @ p )
| sk1 ),
inference(simp,[status(thm)],[406]) ).
thf(448,plain,
! [A: $i] :
( ( ( sk5 @ sk7 )
!= A )
| ( sk5 != initial_world )
| ~ ( A @ sk7 @ p )
| sk1 ),
inference(simp,[status(thm)],[407]) ).
thf(451,plain,
( ( sk5 != initial_world )
| ~ ( sk5 @ sk7 @ sk7 @ p )
| sk1 ),
inference(simp,[status(thm)],[448]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ reachable ) )
& ( B @ ( A @ reachable ) ) )
=> ( C @ ( A @ reachable ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_reachable) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ reachable ) )
& ( B @ ( A @ reachable ) ) )
=> ( C @ ( A @ reachable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk7 @ p )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[25,21]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ reachable ) )
!= ( B @ ( initial_world @ reachable ) ) )
| ~ ( B @ sk7 @ p )
| sk1 ),
inference(simp,[status(thm)],[408]) ).
thf(410,plain,
( ~ ( initial_world @ sk7 @ p )
| sk1 ),
inference(pattern_uni,[status(thm)],[409:[bind(A,$thf( initial_world )),bind(B,$thf( initial_world ))]]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ sk1
| ( A @ ( B @ sk4 ) @ ( B @ reachable ) )
| ~ ( B @ ( A @ sk3 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ sk1
| ( A @ ( B @ sk4 ) @ ( B @ reachable ) )
| ~ ( B @ ( A @ sk3 @ reachable ) )
| ~ ( A @ ( initial_world @ reachable ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(1626,plain,
$false,
inference(e,[status(thm)],[88,106,229,193,13,22,223,194,18,11,239,5,440,10,142,24,25,20,421,228,57,70,21,166,161,180,17,375,362,451,76,103,66,26,23,410,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN550+1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % 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
% 0.13/0.40 % Computer : n007.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 18:10:40 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.69/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.92/0.81 % [INFO] Parsing done (93ms).
% 0.92/0.82 % [INFO] Running in sequential loop mode.
% 1.15/1.02 % [INFO] eprover registered as external prover.
% 1.15/1.03 % [INFO] Scanning for conjecture ...
% 1.44/1.07 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.44/1.09 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.44/1.10 % [INFO] Problem is first-order (TPTP FOF).
% 1.44/1.10 % [INFO] Type checking passed.
% 1.44/1.10 % [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 ...
% 13.01/3.62 % External prover 'e' found a proof!
% 13.01/3.62 % [INFO] Killing All external provers ...
% 13.01/3.62 % Time passed: 3119ms (effective reasoning time: 2801ms)
% 13.01/3.62 % 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)>
% 13.01/3.62 % Axioms used in derivation (2): reflexivity_of_reachable, transitivity_of_reachable
% 13.01/3.62 % No. of inferences in proof: 107
% 13.01/3.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3119 ms resp. 2801 ms w/o parsing
% 11.50/3.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.50/3.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------