%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO886_4.111 : TPTP v9.3.1. Released v9.0.0.
% 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 : n018.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 09:45:32 AM UTC 2026
% Result : Theorem 3.54s 2.31s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 2 ~; 0 |; 2 &; 40 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 3 ( 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 : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(f_decl,type,
f: '$world' > $i > $o ).
thf(1,conjecture,
( ! [A: $i,B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ f ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] : ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ f ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] : ( B @ ( A @ f ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( ! [A: $i,B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ f ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] : ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '$world'] : ( A @ ( A @ '$accessible_world' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(10,plain,
! [A: '$world'] : ( A @ ( A @ '$accessible_world' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: '$world',B: '$world',C: '$world'] :
( ( ( C @ ( B @ '$accessible_world' ) )
& ( B @ ( A @ '$accessible_world' ) ) )
=> ( C @ ( A @ '$accessible_world' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(12,plain,
! [A: '$world',B: '$world',C: '$world'] :
( ( ( C @ ( B @ '$accessible_world' ) )
& ( B @ ( A @ '$accessible_world' ) ) )
=> ( C @ ( A @ '$accessible_world' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
$false,
inference(e,[status(thm)],[5,10,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO886_4.111 : TPTP v9.3.1. Released v9.0.0.
% 0.00/0.08 % 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
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 20:14:37 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.16 % [INFO] Parsing done (180ms).
% 1.27/1.19 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.41/1.20 %%% 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.
% 1.57/1.32 % [INFO] Running in sequential loop mode.
% 2.21/1.70 % [INFO] eprover registered as external prover.
% 2.21/1.71 % [INFO] Scanning for conjecture ...
% 2.21/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.38/1.83 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.38/1.84 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.38/1.84 % [INFO] Type checking passed.
% 2.38/1.85 % [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 ...
% 3.54/2.31 % External prover 'e' found a proof!
% 3.54/2.31 % [INFO] Killing All external provers ...
% 3.54/2.31 % Time passed: 1760ms (effective reasoning time: 980ms)
% 3.54/2.31 % 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)>
% 3.54/2.31 % Axioms used in derivation (2): mrel_reflexive, mrel_transitive
% 3.54/2.31 % No. of inferences in proof: 8
% 3.54/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1760 ms resp. 980 ms w/o parsing
% 3.54/2.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.54/2.35 % [INFO] Killing All external provers ...
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