%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL955^24 : TPTP v9.3.1. Released v8.1.0.
% 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 : n005.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 : Wed Sep 30 08:14:19 AM UTC 2026
% Result : Theorem 26.83s 10.44s
% Output : Refutation 27.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 31 ( 19 unt; 0 typ; 11 def)
% Number of atoms : 151 ( 11 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 332 ( 34 ~; 19 |; 13 &; 227 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 13 con; 0-3 aty)
% Number of variables : 54 ( 12 ^; 36 !; 0 ?; 54 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mnot_decl,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mand_decl,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(true_decl,type,
true: mworld > $o ).
thf(tptp_float_0_001_decl,type,
tptp_float_0_001: $i ).
thf(loopcounter_decl,type,
loopcounter: $i ).
thf(pv65_decl,type,
pv65: $i ).
thf(n1_decl,type,
n1: $i ).
thf(geq_decl,type,
geq: $i > $i > mworld > $o ).
thf(gt_decl,type,
gt: $i > $i > mworld > $o ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(sk1_decl,type,
sk1: mworld ).
thf(sk2_decl,type,
sk2: $o ).
thf(sk3_decl,type,
sk3: mworld ).
thf(sk4_decl,type,
sk4: mworld > mworld ).
thf(sk5_decl,type,
sk5: mworld ).
thf(sk6_decl,type,
sk6: mworld ).
thf(sk7_decl,type,
sk7: mworld ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: mworld] :
~ ( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( geq @ pv65 @ tptp_float_0_001 @ B ) )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ~ ! [D: mworld] :
( ( mrel @ C @ D )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ D ) ) )
=> ! [C: mworld] :
( ( mrel @ B @ C )
=> ( true @ C ) ) ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ C ) )
=> ! [C: mworld] :
( ( mrel @ B @ C )
=> ( true @ C ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: mworld] :
~ ( ( mrel @ sk1 @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ~ ! [C: mworld] :
( ( mrel @ B @ C )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ C ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( true @ B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: mworld] :
~ ( ( mrel @ sk3 @ A )
=> ( true @ A ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: mworld] :
~ ( ( mrel @ sk1 @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( true @ B ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: mworld] :
~ ( ( mrel @ sk6 @ A )
=> ( true @ A ) ) ) ) ).
thf(1,conjecture,
mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( geq @ pv65 @ tptp_float_0_001 ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( gt @ ( plus @ n1 @ loopcounter ) @ n1 ) ) ) ) @ ( mbox @ true ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( gt @ ( plus @ n1 @ loopcounter ) @ n1 ) ) @ ( mbox @ true ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_array_0028) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( geq @ pv65 @ tptp_float_0_001 ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( gt @ ( plus @ n1 @ loopcounter ) @ n1 ) ) ) ) @ ( mbox @ true ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( gt @ ( plus @ n1 @ loopcounter ) @ n1 ) ) @ ( mbox @ true ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(139,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( geq @ pv65 @ tptp_float_0_001 @ B ) )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ~ ! [D: mworld] :
( ( mrel @ C @ D )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ D ) ) )
=> ! [C: mworld] :
( ( mrel @ B @ C )
=> ( true @ C ) ) ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ C ) )
=> ! [C: mworld] :
( ( mrel @ B @ C )
=> ( true @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(140,plain,
! [C: mworld,B: mworld,A: mworld] :
( ( mrel @ mactual @ sk1 )
& ( ~ ( mrel @ sk1 @ A )
| ( geq @ pv65 @ tptp_float_0_001 @ A ) )
& ( ( mrel @ sk1 @ sk3 )
| ~ sk2 )
& ( ~ ( mrel @ sk3 @ B )
| ( mrel @ B @ ( sk4 @ B ) )
| ~ sk2 )
& ( ~ ( mrel @ sk3 @ B )
| ~ ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ ( sk4 @ B ) )
| ~ sk2 )
& ( ( mrel @ sk3 @ sk5 )
| ~ sk2 )
& ( ~ ( true @ sk5 )
| ~ sk2 )
& ( sk2
| ( mrel @ sk1 @ sk6 ) )
& ( sk2
| ~ ( mrel @ sk6 @ C )
| ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ C ) )
& ( sk2
| ( mrel @ sk6 @ sk7 ) )
& ( sk2
| ~ ( true @ sk7 ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(145,plain,
( ~ ( true @ sk5 )
| ~ sk2 ),
inference(cnfConj,[status(thm)],[140]) ).
thf(10,axiom,
mlocal @ ( mbox @ true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ttrue) ).
thf(187,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( true @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(188,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( true @ A ) ),
inference(cnf,[status(esa)],[187]) ).
thf(76,axiom,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(658,plain,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(659,plain,
! [B: mworld,A: mworld] : ( mrel @ A @ B ),
inference(cnf,[status(esa)],[658]) ).
thf(996,plain,
! [A: mworld] :
( ~ $true
| ( true @ A ) ),
inference(rewrite,[status(thm)],[188,659]) ).
thf(997,plain,
! [A: mworld] : ( true @ A ),
inference(simp,[status(thm)],[996]) ).
thf(1000,plain,
( ~ $true
| ~ sk2 ),
inference(rewrite,[status(thm)],[145,997]) ).
thf(1001,plain,
~ sk2,
inference(simp,[status(thm)],[1000]) ).
thf(147,plain,
( sk2
| ~ ( true @ sk7 ) ),
inference(cnfConj,[status(thm)],[140]) ).
thf(998,plain,
( sk2
| ~ $true ),
inference(rewrite,[status(thm)],[147,997]) ).
thf(999,plain,
sk2,
inference(simp,[status(thm)],[998]) ).
thf(1004,plain,
~ $true,
inference(rewrite,[status(thm)],[1001,999]) ).
thf(1005,plain,
$false,
inference(simp,[status(thm)],[1004]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL955^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.10 % 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
% 0.09/0.29 % Computer : n005.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8046.5625MB
% 0.09/0.29 % OS : Linux 6.8.0-71-generic
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Sep 29 10:54:01 UTC 2026
% 0.26/0.29 % CPUTime :
% 0.26/0.29 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
% 1.23/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.46/1.39 % [INFO] Parsing done (454ms).
% 2.89/1.41 % [INFO] Running in sequential loop mode.
% 4.14/1.85 % [INFO] eprover registered as external prover.
% 4.14/1.86 % [INFO] Scanning for conjecture ...
% 4.92/2.13 % [INFO] Found a conjecture (or negated_conjecture) and 136 axioms. Running axiom selection ...
% 5.82/2.37 % [INFO] Axiom selection finished. Selected 136 axioms (removed 0 axioms).
% 6.74/2.67 % [INFO] Problem is higher-order (TPTP THF).
% 7.04/2.70 % [INFO] Type checking passed.
% 7.04/2.71 % [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 ...
% 26.83/10.43 % [INFO] Killing All external provers ...
% 26.83/10.43 % Time passed: 9973ms (effective reasoning time: 9017ms)
% 26.83/10.44 % 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)>
% 26.83/10.44 % Axioms used in derivation (2): ttrue, mrel_universal
% 26.83/10.44 % No. of inferences in proof: 20
% 26.83/10.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9973 ms resp. 9017 ms w/o parsing
% 27.26/10.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.26/10.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------