%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO983_1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 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 : n002.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 3.54s 2.30s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 45 ( 22 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 81 ( 9 ~; 0 |; 10 &; 44 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 12 !; 3 ?; 18 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf('$exists_in_world_$i_decl',type,
'$exists_in_world_$i': '$world' > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: '$world' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ( ( A = B )
=> ( ? [C: '$world'] : ( C @ ( '$local_world' @ '$accessible_world' ) )
=> ( A = B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ ( '$local_world' @ '$exists_in_world_$i' ) )
& ( sk1 @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ( ( sk1 = A )
=> ( ? [B: '$world'] : ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( sk1 = A ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: '$world'] : ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ( ( A = B )
=> ! [C: '$world'] :
( ( C @ ( '$local_world' @ '$accessible_world' ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',example) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ( ( A = B )
=> ! [C: '$world'] :
( ( C @ ( '$local_world' @ '$accessible_world' ) )
=> ( A = B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ( ( A = B )
=> ! [C: '$world'] :
( ( C @ ( '$local_world' @ '$accessible_world' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( '$local_world' @ '$exists_in_world_$i' ) )
& ( A @ ( '$local_world' @ '$exists_in_world_$i' ) ) )
=> ( ( A = B )
=> ( ? [C: '$world'] : ( C @ ( '$local_world' @ '$accessible_world' ) )
=> ( A = B ) ) ) ),
inference(miniscope,[status(thm)],[4]) ).
thf(6,plain,
( ( sk1 != sk2 )
& ( sk3 @ ( '$local_world' @ '$accessible_world' ) )
& ( sk1 = sk2 )
& ( sk2 @ ( '$local_world' @ '$exists_in_world_$i' ) )
& ( sk1 @ ( '$local_world' @ '$exists_in_world_$i' ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(11,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[6]) ).
thf(13,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[11]) ).
thf(7,plain,
sk1 = sk2,
inference(cnfConj,[status(thm)],[6]) ).
thf(12,plain,
sk2 = sk1,
inference(lifteq,[status(thm)],[7]) ).
thf(16,plain,
sk1 != sk1,
inference(rewrite,[status(thm)],[13,12]) ).
thf(17,plain,
$false,
inference(simp,[status(thm)],[16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO983_1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 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
% 0.16/0.41 % Computer : n002.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 20:23:20 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.18 % [INFO] Parsing done (181ms).
% 1.41/1.20 % [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.
% 1.57/1.33 % [INFO] Running in sequential loop mode.
% 2.20/1.70 % [INFO] eprover registered as external prover.
% 2.20/1.71 % [INFO] Scanning for conjecture ...
% 2.38/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.38/1.84 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.38/1.84 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.38/1.85 % [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 ...
% 3.26/2.29 % [INFO] Killing All external provers ...
% 3.54/2.30 % Time passed: 1737ms (effective reasoning time: 964ms)
% 3.54/2.30 % 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)>
% 3.54/2.30 % Axioms used in derivation (0):
% 3.54/2.30 % No. of inferences in proof: 11
% 3.54/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1737 ms resp. 964 ms w/o parsing
% 3.54/2.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.54/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------