%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0.
% 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 : 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 07:53:29 AM UTC 2026
% Result : Theorem 3.37s 2.34s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 136 ( 11 ~; 0 |; 4 &; 100 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 0 ^; 29 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf('$ki_world_type',type,
'$ki_world': $tType ).
thf('$ki_index_type',type,
'$ki_index': $tType ).
thf('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
thf('$ki_accessible_decl',type,
'$ki_accessible': '$ki_index' > '$ki_world' > '$ki_world' > $o ).
thf('#idx(a)_decl',type,
'#idx(a)': '$ki_index' ).
thf('#idx(b)_decl',type,
'#idx(b)': '$ki_index' ).
thf(p_decl,type,
p: '$ki_world' > $o ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(a)' @ '$ki_accessible' ) ) )
=> ~ ( A @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(a)' @ '$ki_accessible' ) ) )
=> ~ ( A @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(a)' @ '$ki_accessible' ) ) )
=> ~ ( A @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
( ~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b)' @ '$ki_accessible' ) ) )
=> ( A @ p ) )
=> ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(a)' @ '$ki_accessible' ) ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) )
=> ( B @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_2) ).
thf(24,plain,
( ~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b)' @ '$ki_accessible' ) ) )
=> ( A @ p ) )
=> ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(a)' @ '$ki_accessible' ) ) )
=> ~ ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) )
=> ( B @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: '$ki_world'] : ( A @ ( A @ ( '#idx(a)' @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive_#idx(a)') ).
thf(14,plain,
! [A: '$ki_world'] : ( A @ ( A @ ( '#idx(a)' @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ ( '#idx(b)' @ '$ki_accessible' ) ) )
& ( B @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) ) )
=> ( C @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_transitive_#idx(b)') ).
thf(20,plain,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ ( '#idx(b)' @ '$ki_accessible' ) ) )
& ( B @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) ) )
=> ( C @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
~ ( '$ki_local_world' @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_a_axiom_1) ).
thf(28,plain,
~ ( '$ki_local_world' @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(a)' @ '$ki_accessible' ) ) )
=> ( ( A @ p )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) )
=> ( B @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_axiom_1) ).
thf(22,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(a)' @ '$ki_accessible' ) ) )
=> ( ( A @ p )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) )
=> ( B @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: '$ki_world'] : ( A @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_reflexive_#idx(b)') ).
thf(18,plain,
! [A: '$ki_world'] : ( A @ ( A @ ( '#idx(b)' @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ ( '#idx(a)' @ '$ki_accessible' ) ) )
& ( B @ ( A @ ( '#idx(a)' @ '$ki_accessible' ) ) ) )
=> ( C @ ( A @ ( '#idx(a)' @ '$ki_accessible' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_transitive_#idx(a)') ).
thf(16,plain,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ ( '#idx(a)' @ '$ki_accessible' ) ) )
& ( B @ ( A @ ( '#idx(a)' @ '$ki_accessible' ) ) ) )
=> ( C @ ( A @ ( '#idx(a)' @ '$ki_accessible' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[10,24,14,20,28,22,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL962_16 : TPTP v9.3.1. Released v8.2.0.
% 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
% 0.14/0.40 % Computer : n007.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 23:50:08 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.82/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.18 % [INFO] Parsing done (192ms).
% 1.17/1.19 % [INFO] Running in sequential loop mode.
% 1.79/1.59 % [INFO] eprover registered as external prover.
% 1.79/1.60 % [INFO] Scanning for conjecture ...
% 1.98/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.13/1.74 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.13/1.76 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.13/1.77 % [INFO] Type checking passed.
% 2.13/1.77 % [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 ...
% 3.37/2.34 % External prover 'e' found a proof!
% 3.37/2.34 % [INFO] Killing All external provers ...
% 3.37/2.34 % Time passed: 1801ms (effective reasoning time: 1145ms)
% 3.37/2.34 % 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)>
% 3.37/2.34 % Axioms used in derivation (7): ab_axiom_2, ab_axiom_1, mrel_reflexive_#idx(a), mrel_transitive_#idx(b), not_a_axiom_1, mrel_reflexive_#idx(b), mrel_transitive_#idx(a)
% 3.37/2.34 % No. of inferences in proof: 18
% 3.37/2.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1801 ms resp. 1145 ms w/o parsing
% 3.37/2.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.37/2.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------