%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ001_8 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 08:21:02 AM UTC 2026
% Result : Theorem 2.71s 1.52s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 4 unt; 0 typ; 1 def)
% Number of atoms : 25 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 58 ( 6 ~; 0 |; 7 &; 37 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 16 ( 0 ^; 10 !; 5 ?; 16 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(person_type,type,
person: $tType ).
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(agatha_decl,type,
agatha: person ).
thf(lives_decl,type,
lives: '$world' > person > $o ).
thf(killed_decl,type,
killed: '$world' > person > person > $o ).
thf(sk1_decl,type,
sk1: '$world' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: '$world'] : ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ).
thf(1,conjecture,
? [A: person] :
( ( ( agatha @ ( A @ ( '$local_world' @ killed ) ) )
& ( A @ ( '$local_world' @ lives ) ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A = agatha ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel55) ).
thf(2,negated_conjecture,
~ ? [A: person] :
( ( ( agatha @ ( A @ ( '$local_world' @ killed ) ) )
& ( A @ ( '$local_world' @ lives ) ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A = agatha ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ? [A: person] :
( ( ( agatha @ ( A @ ( '$local_world' @ killed ) ) )
& ( A @ ( '$local_world' @ lives ) ) )
=> ! [B: '$world'] :
( ( B @ ( '$local_world' @ '$accessible_world' ) )
=> ( A = agatha ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
~ ( ( ! [A: person] : ( agatha @ ( A @ ( '$local_world' @ killed ) ) )
& ! [A: person] : ( A @ ( '$local_world' @ lives ) ) )
=> ( ? [A: '$world'] : ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ? [A: person] : ( A = agatha ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [C: person,B: person,A: person] :
( ( C != agatha )
& ( sk1 @ ( '$local_world' @ '$accessible_world' ) )
& ( agatha @ ( B @ ( '$local_world' @ killed ) ) )
& ( A @ ( '$local_world' @ lives ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(25,plain,
! [A: person] : ( A != agatha ),
inference(cnfConj,[status(thm)],[21]) ).
thf(27,plain,
! [A: person] : ( A != agatha ),
inference(lifteq,[status(thm)],[25]) ).
thf(28,plain,
$false,
inference(simp,[status(thm)],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ001_8 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 05:02:51 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.93/0.83 % [INFO] Parsing done (103ms).
% 0.93/0.84 % [INFO] Input problem is non-classical (logic $alethic_modal). Running HOL transformation from semantics specification contained in the problem file ...
% 0.93/0.85 %%% 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.
% 1.22/0.91 % [INFO] Running in sequential loop mode.
% 1.64/1.09 % [INFO] eprover registered as external prover.
% 1.64/1.09 % [INFO] Scanning for conjecture ...
% 1.91/1.13 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 1.91/1.17 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.13/1.20 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.13/1.21 % [INFO] Type checking passed.
% 2.13/1.21 % [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 ...
% 2.71/1.52 % [INFO] Killing All external provers ...
% 2.71/1.52 % Time passed: 1010ms (effective reasoning time: 607ms)
% 2.71/1.52 % 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)>
% 2.71/1.52 % Axioms used in derivation (0):
% 2.71/1.52 % No. of inferences in proof: 8
% 2.71/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1010 ms resp. 607 ms w/o parsing
% 2.71/1.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.71/1.57 % [INFO] Killing All external provers ...
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