%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL957^6 : 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 08:14:20 AM UTC 2026
% Result : Theorem 5.94s 3.25s
% Output : Refutation 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 5 def)
% Number of atoms : 69 ( 5 equ; 0 cnn)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 116 ( 2 ~; 0 |; 0 &; 100 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 38 ( 18 ^; 17 !; 3 ?; 38 :)
% 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(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_decl,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(big_r_decl,type,
big_r: $i > $i > mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
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(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] : ( A @ C @ B ) ) ) ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] : ( A @ C @ B ) ) ) ).
thf(1,conjecture,
( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( big_r @ A @ A ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( big_r @ A @ A ) ) ) ) ) )
@ ( mexists_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ A @ A ) ) @ ( mbox @ ( big_r @ B @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2122) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [A: $i] : ( mbox @ ( big_r @ A @ A ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( big_r @ A @ A ) ) ) ) ) )
@ ( mexists_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_r @ A @ A ) ) @ ( mbox @ ( big_r @ B @ B ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( ? [C: $i] :
! [D: mworld] :
( ( mrel @ B @ D )
=> ( big_r @ C @ C @ D ) )
=> ! [C: mworld] :
( ( mrel @ B @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( big_r @ D @ D @ E ) ) ) ) )
=> ? [B: $i] :
! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( big_r @ B @ B @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( big_r @ D @ D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(19,plain,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[4,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL957^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.12 % 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
% 0.28/0.33 % Computer : n005.cluster.edu
% 0.28/0.33 % Model : x86_64 x86_64
% 0.28/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.33 % Memory : 8046.5625MB
% 0.28/0.33 % OS : Linux 6.8.0-71-generic
% 0.28/0.33 % CPULimit : 300
% 0.28/0.33 % WCLimit : 300
% 0.28/0.33 % DateTime : Tue Sep 29 10:58:01 UTC 2026
% 0.28/0.33 % CPUTime :
% 0.28/0.33 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
% 1.51/1.17 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.48 % [INFO] Parsing done (303ms).
% 2.27/1.50 % [INFO] Running in sequential loop mode.
% 3.23/2.11 % [INFO] eprover registered as external prover.
% 3.23/2.13 % [INFO] Scanning for conjecture ...
% 3.70/2.31 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 3.70/2.36 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 3.70/2.37 % [INFO] Problem is higher-order (TPTP THF).
% 3.70/2.37 % [INFO] Type checking passed.
% 3.70/2.38 % [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 ...
% 5.94/3.24 % External prover 'e' found a proof!
% 5.94/3.24 % [INFO] Killing All external provers ...
% 5.94/3.24 % Time passed: 2707ms (effective reasoning time: 1736ms)
% 5.94/3.24 % 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)>
% 5.94/3.25 % Axioms used in derivation (1): mrel_universal
% 5.94/3.25 % No. of inferences in proof: 6
% 5.94/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2707 ms resp. 1736 ms w/o parsing
% 6.17/3.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.17/3.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------