%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO976_1 : TPTP v9.3.1. Released v9.1.0.
% 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 : n020.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 09:45:51 AM UTC 2026
% Result : Theorem 3.48s 2.38s
% Output : Refutation 3.71s
% 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 : 29 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 79 ( 2 ~; 0 |; 3 &; 56 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 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 : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(p_decl,type,
p: '$world' > $i > $o ).
thf(1,conjecture,
( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i,C: '$world'] :
( ( C @ ( A @ '$accessible_world' ) )
=> ( B @ ( C @ p ) ) ) )
<=> ! [A: $i,B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exercise1) ).
thf(2,negated_conjecture,
~ ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i,C: '$world'] :
( ( C @ ( A @ '$accessible_world' ) )
=> ( B @ ( C @ p ) ) ) )
<=> ! [A: $i,B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( ( ! [A: $i,B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i,C: '$world'] :
( ( C @ ( A @ '$accessible_world' ) )
=> ( B @ ( C @ p ) ) ) ) )
& ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i,C: '$world'] :
( ( C @ ( A @ '$accessible_world' ) )
=> ( B @ ( C @ p ) ) ) )
=> ! [A: $i,B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '$world'] : ( A @ ( A @ '$accessible_world' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(17,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(19,plain,
$false,
inference(e,[status(thm)],[5,15,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO976_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 20:21:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.17 % [INFO] Parsing done (184ms).
% 1.26/1.19 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.41/1.21 %%% 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.
% 1.56/1.33 % [INFO] Running in sequential loop mode.
% 2.20/1.71 % [INFO] eprover registered as external prover.
% 2.20/1.72 % [INFO] Scanning for conjecture ...
% 2.37/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.37/1.84 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.37/1.85 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.37/1.85 % [INFO] Type checking passed.
% 2.37/1.86 % [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 ...
% 3.48/2.38 % External prover 'e' found a proof!
% 3.48/2.38 % [INFO] Killing All external provers ...
% 3.48/2.38 % Time passed: 1842ms (effective reasoning time: 1043ms)
% 3.48/2.38 % 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)>
% 3.48/2.38 % Axioms used in derivation (2): mrel_reflexive, mrel_transitive
% 3.48/2.38 % No. of inferences in proof: 8
% 3.48/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1842 ms resp. 1043 ms w/o parsing
% 3.71/2.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------