%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO994_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 : n014.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 5.51s 7.96s
% Output : Refutation 5.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 0 equ; 0 cnn)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 206 ( 2 ~; 0 |; 0 &; 142 @)
% ( 0 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 ^; 53 !; 2 ?; 55 :)
% 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 > $o ).
thf(1,conjecture,
( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$exists_in_world_$i' ) )
=> ( ! [D: $i] :
( ( D @ ( B @ '$exists_in_world_$i' ) )
=> ! [E: '$world'] :
( ( E @ ( B @ '$accessible_world' ) )
=> ( D @ ( E @ p ) ) ) )
=> ! [D: '$world'] :
( ( D @ ( B @ '$accessible_world' ) )
=> ( C @ ( D @ p ) ) ) ) ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ! [C: '$world'] :
( ( C @ ( A @ '$accessible_world' ) )
=> ( ! [D: $i] :
( ( D @ ( C @ '$exists_in_world_$i' ) )
=> ! [E: '$world'] :
( ( E @ ( C @ '$accessible_world' ) )
=> ( D @ ( E @ p ) ) ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( B @ ( D @ p ) ) ) ) ) ) ) )
=> ( ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exercise) ).
thf(2,negated_conjecture,
~ ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$exists_in_world_$i' ) )
=> ( ! [D: $i] :
( ( D @ ( B @ '$exists_in_world_$i' ) )
=> ! [E: '$world'] :
( ( E @ ( B @ '$accessible_world' ) )
=> ( D @ ( E @ p ) ) ) )
=> ! [D: '$world'] :
( ( D @ ( B @ '$accessible_world' ) )
=> ( C @ ( D @ p ) ) ) ) ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ! [C: '$world'] :
( ( C @ ( A @ '$accessible_world' ) )
=> ( ! [D: $i] :
( ( D @ ( C @ '$exists_in_world_$i' ) )
=> ! [E: '$world'] :
( ( E @ ( C @ '$accessible_world' ) )
=> ( D @ ( E @ p ) ) ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( B @ ( D @ p ) ) ) ) ) ) ) )
=> ( ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( ! [B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ! [C: $i] :
( ( C @ ( B @ '$exists_in_world_$i' ) )
=> ( ! [D: $i] :
( ( D @ ( B @ '$exists_in_world_$i' ) )
=> ! [E: '$world'] :
( ( E @ ( B @ '$accessible_world' ) )
=> ( D @ ( E @ p ) ) ) )
=> ! [D: '$world'] :
( ( D @ ( B @ '$accessible_world' ) )
=> ( C @ ( D @ p ) ) ) ) ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ! [C: '$world'] :
( ( C @ ( A @ '$accessible_world' ) )
=> ( ! [D: $i] :
( ( D @ ( C @ '$exists_in_world_$i' ) )
=> ! [E: '$world'] :
( ( E @ ( C @ '$accessible_world' ) )
=> ( D @ ( E @ p ) ) ) )
=> ! [D: '$world'] :
( ( D @ ( C @ '$accessible_world' ) )
=> ( B @ ( D @ p ) ) ) ) ) ) ) )
=> ( ! [A: $i] :
( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A @ ( B @ p ) ) ) )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '$world'] : ( A @ ( A @ '$accessible_world' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(24,plain,
! [A: '$world'] : ( A @ ( A @ '$accessible_world' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: '$world',B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( A @ ( B @ '$accessible_world' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_symmetric) ).
thf(26,plain,
! [A: '$world',B: '$world'] :
( ( B @ ( A @ '$accessible_world' ) )
=> ( A @ ( B @ '$accessible_world' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: '$world'] :
? [B: $i] : ( B @ ( A @ '$exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$exists_in_world_$i_nonempty') ).
thf(28,plain,
! [A: '$world'] :
? [B: $i] : ( B @ ( A @ '$exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(169,plain,
$false,
inference(e,[status(thm)],[6,24,26,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO994_1 : TPTP v9.3.1. Released v9.1.0.
% 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
% 0.13/5.41 % Computer : n014.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Sat Sep 26 20:21:08 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 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
% 0.17/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/6.18 % [INFO] Parsing done (181ms).
% 1.35/6.20 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.35/6.22 %%% 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.
% 1.50/6.34 % [INFO] Running in sequential loop mode.
% 2.17/6.73 % [INFO] eprover registered as external prover.
% 2.17/6.74 % [INFO] Scanning for conjecture ...
% 2.33/6.83 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.33/6.87 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.33/6.89 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.33/6.89 % [INFO] Type checking passed.
% 2.57/6.90 % [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 ...
% 5.51/7.95 % External prover 'e' found a proof!
% 5.51/7.95 % [INFO] Killing All external provers ...
% 5.51/7.95 % Time passed: 2395ms (effective reasoning time: 1603ms)
% 5.51/7.95 % 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)>
% 5.51/7.96 % Axioms used in derivation (3): mrel_reflexive, mrel_symmetric, $exists_in_world_$i_nonempty
% 5.51/7.96 % No. of inferences in proof: 10
% 5.51/7.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2395 ms resp. 1603 ms w/o parsing
% 5.51/7.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.51/7.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------