%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO990_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 : 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 09:45:52 AM UTC 2026
% Result : Theorem 1.62s 1.26s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 3 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 87 ( 2 ~; 0 |; 3 &; 58 @)
% ( 0 <=>; 24 =>; 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 : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 20 !; 5 ?; 25 :)
% 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 > $o ).
thf('$exists_in_world_$i_decl',type,
'$exists_in_world_$i': '$world' > $i > $o ).
thf(1,conjecture,
( ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ? [C: $i] :
( ( C = A )
& ( C @ ( B @ '$exists_in_world_$i' ) ) ) ) )
=> ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) ) )
=> ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exercise) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ? [C: $i] :
( ( C = A )
& ( C @ ( B @ '$exists_in_world_$i' ) ) ) ) )
=> ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) ) )
=> ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ? [C: $i] :
( ( C = A )
& ( C @ ( B @ '$exists_in_world_$i' ) ) ) ) )
=> ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) ) )
=> ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$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'] :
? [B: $i] : ( B @ ( A @ '$exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$exists_in_world_$i_nonempty') ).
thf(14,plain,
! [A: '$world'] :
? [B: $i] : ( B @ ( A @ '$exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[4,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO990_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % 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
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 20:20:34 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 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
% 0.38/0.60 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.69 % [INFO] Parsing done (84ms).
% 0.66/0.70 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 0.66/0.70 %%% 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.
% 0.66/0.76 % [INFO] Running in sequential loop mode.
% 0.98/0.93 % [INFO] eprover registered as external prover.
% 0.98/0.93 % [INFO] Scanning for conjecture ...
% 0.98/0.98 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 0.98/1.00 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 0.98/1.00 % [INFO] Problem is typed first-order (TPTP TFF).
% 0.98/1.00 % [INFO] Type checking passed.
% 0.98/1.01 % [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 ...
% 1.62/1.26 % External prover 'e' found a proof!
% 1.62/1.26 % [INFO] Killing All external provers ...
% 1.62/1.26 % Time passed: 869ms (effective reasoning time: 500ms)
% 1.62/1.26 % 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)>
% 1.62/1.26 % Axioms used in derivation (1): $exists_in_world_$i_nonempty
% 1.62/1.26 % No. of inferences in proof: 6
% 1.62/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 869 ms resp. 500 ms w/o parsing
% 1.62/1.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.62/1.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------