%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO982_1 : TPTP v9.3.1. Bugfixed v9.3.0.
% 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 09:45:52 AM UTC 2026
% Result : Theorem 3.24s 2.25s
% Output : Refutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 22 ( 15 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 36 ( 14 ~; 0 |; 2 &; 12 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 5 ( 0 ^; 3 !; 1 ?; 5 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% 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(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(sk1_decl,type,
sk1: '$world' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: '$world'] : ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ).
thf(1,conjecture,
( ( x != y )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( x != y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exercise2) ).
thf(2,negated_conjecture,
~ ( ( x != y )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( x != y ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( x != y )
=> ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( x != y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( x != y )
=> ( ? [A: '$world'] : ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ( x != y ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
( ( x = y )
& ( sk1 @ ( '$local_world' @ '$accessible_world' ) )
& ( x != y ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
x = y,
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
y = x,
inference(lifteq,[status(thm)],[8]) ).
thf(6,plain,
x != y,
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
y != x,
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
$false,
inference(simplifyReflect,[status(thm)],[10,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO982_1 : TPTP v9.3.1. Bugfixed v9.3.0.
% 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 : n014.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 20:20:31 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 ...
% 1.28/1.16 % [INFO] Parsing done (180ms).
% 1.28/1.18 % [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.
% 1.41/1.29 % [INFO] Running in sequential loop mode.
% 2.02/1.67 % [INFO] eprover registered as external prover.
% 2.02/1.68 % [INFO] Scanning for conjecture ...
% 2.20/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.38/1.80 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.38/1.81 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.38/1.81 % [INFO] Type checking passed.
% 2.38/1.82 % [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 ...
% 3.24/2.24 % [INFO] Killing All external provers ...
% 3.24/2.25 % Time passed: 1713ms (effective reasoning time: 951ms)
% 3.24/2.25 % 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)>
% 3.24/2.25 % Axioms used in derivation (0):
% 3.24/2.25 % No. of inferences in proof: 10
% 3.24/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1713 ms resp. 951 ms w/o parsing
% 3.24/2.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.24/2.29 % [INFO] Killing All external provers ...
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