%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO996_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 : n012.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 09:45:53 AM UTC 2026
% Result : Theorem 1.68s 1.21s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 41 ( 2 ~; 0 |; 0 &; 26 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(x_decl,type,
x: '$world' > $o ).
thf(1,conjecture,
( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ x ) ) )
=> ( '$local_world' @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ x ) ) )
=> ( '$local_world' @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ x ) ) )
=> ( '$local_world' @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '$world'] :
( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ x ) )
=> ( A @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(8,plain,
! [A: '$world'] :
( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( B @ x ) )
=> ( A @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
$false,
inference(e,[status(thm)],[4,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO996_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % 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
% 0.07/0.32 % Computer : n012.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8046.5625MB
% 0.07/0.32 % OS : Linux 6.8.0-71-generic
% 0.07/0.32 % CPULimit : 300
% 0.07/0.32 % WCLimit : 300
% 0.07/0.32 % DateTime : Sat Sep 26 20:21:18 UTC 2026
% 0.07/0.32 % CPUTime :
% 0.07/0.32 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
% 0.41/0.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.69 % [INFO] Parsing done (81ms).
% 0.68/0.70 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 0.68/0.71 %%% 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.
% 0.68/0.75 % [INFO] Running in sequential loop mode.
% 0.98/0.92 % [INFO] eprover registered as external prover.
% 0.98/0.92 % [INFO] Scanning for conjecture ...
% 0.98/0.96 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 0.98/0.98 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 0.98/0.98 % [INFO] Problem is typed first-order (TPTP TFF).
% 0.98/0.99 % [INFO] Type checking passed.
% 0.98/0.99 % [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 ...
% 1.68/1.21 % External prover 'e' found a proof!
% 1.68/1.21 % [INFO] Killing All external provers ...
% 1.68/1.21 % Time passed: 813ms (effective reasoning time: 453ms)
% 1.68/1.21 % 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)>
% 1.68/1.21 % Axioms used in derivation (1): ax1
% 1.68/1.21 % No. of inferences in proof: 6
% 1.68/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 813 ms resp. 453 ms w/o parsing
% 1.68/1.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.68/1.23 % [INFO] Killing All external provers ...
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