%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NLP265_17 : TPTP v9.3.1. Released v8.2.0.
% 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 : n016.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 08:05:17 AM UTC 2026
% Result : Theorem 2.67s 11.83s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 206 ( 8 ~; 0 |; 4 &; 158 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf('$ki_world_type',type,
'$ki_world': $tType ).
thf('$ki_index_type',type,
'$ki_index': $tType ).
thf('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
thf('$ki_accessible_decl',type,
'$ki_accessible': '$ki_index' > '$ki_world' > '$ki_world' > $o ).
thf('#idx(b_alice)_decl',type,
'#idx(b_alice)': '$ki_index' ).
thf('#idx(b_bob)_decl',type,
'#idx(b_bob)': '$ki_index' ).
thf('#idx(i_bob)_decl',type,
'#idx(i_bob)': '$ki_index' ).
thf('#idx(i_alice)_decl',type,
'#idx(i_alice)': '$ki_index' ).
thf(portland_decl,type,
portland: $i ).
thf(bigcity_decl,type,
bigcity: '$ki_world' > $i > $o ).
thf(7,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ( ( ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ! [C: '$ki_world'] :
( ( C @ ( B @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ~ ( portland @ ( C @ bigcity ) ) ) )
& ( portland @ ( A @ bigcity ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(i_alice)' @ '$ki_accessible' ) ) )
=> ! [C: '$ki_world'] :
( ( C @ ( B @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ( portland @ ( C @ bigcity ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_alice) ).
thf(24,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ( ( ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ! [C: '$ki_world'] :
( ( C @ ( B @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ~ ( portland @ ( C @ bigcity ) ) ) )
& ( portland @ ( A @ bigcity ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(i_alice)' @ '$ki_accessible' ) ) )
=> ! [C: '$ki_world'] :
( ( C @ ( B @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ( portland @ ( C @ bigcity ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ( portland @ ( A @ bigcity ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(34,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ( portland @ ( A @ bigcity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ ( '#idx(i_alice)' @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(i_alice)') ).
thf(22,plain,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ ( '#idx(i_alice)' @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(b_bob)') ).
thf(18,plain,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(b_alice)') ).
thf(16,plain,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(i_alice)' @ '$ki_accessible' ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ( portland @ ( B @ bigcity ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(i_alice)' @ '$ki_accessible' ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ( portland @ ( B @ bigcity ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(i_alice)' @ '$ki_accessible' ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ( portland @ ( B @ bigcity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ~ ( portland @ ( B @ bigcity ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(36,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ~ ( portland @ ( B @ bigcity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ ( '#idx(i_bob)' @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_universal_#idx(i_bob)') ).
thf(20,plain,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ ( '#idx(i_bob)' @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ( ( ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ! [C: '$ki_world'] :
( ( C @ ( B @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ~ ( portland @ ( C @ bigcity ) ) ) )
& ( portland @ ( A @ bigcity ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(i_bob)' @ '$ki_accessible' ) ) )
=> ! [C: '$ki_world'] :
( ( C @ ( B @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ( portland @ ( C @ bigcity ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_bob) ).
thf(29,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ( ( ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(b_bob)' @ '$ki_accessible' ) ) )
=> ! [C: '$ki_world'] :
( ( C @ ( B @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ~ ( portland @ ( C @ bigcity ) ) ) )
& ( portland @ ( A @ bigcity ) ) )
=> ! [B: '$ki_world'] :
( ( B @ ( A @ ( '#idx(i_bob)' @ '$ki_accessible' ) ) )
=> ! [C: '$ki_world'] :
( ( C @ ( B @ ( '#idx(b_alice)' @ '$ki_accessible' ) ) )
=> ( portland @ ( C @ bigcity ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[24,34,22,18,16,11,36,20,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP265_17 : TPTP v9.3.1. Released v8.2.0.
% 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
% 0.14/10.81 % Computer : n016.cluster.edu
% 0.14/10.81 % Model : x86_64 x86_64
% 0.14/10.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.81 % Memory : 8046.5625MB
% 0.14/10.81 % OS : Linux 6.8.0-71-generic
% 0.14/10.81 % CPULimit : 300
% 0.14/10.81 % WCLimit : 300
% 0.14/10.81 % DateTime : Sat Sep 26 01:55:29 UTC 2026
% 0.14/10.82 % CPUTime :
% 0.14/10.82 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
% 0.57/11.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.93/11.22 % [INFO] Parsing done (102ms).
% 0.93/11.22 % [INFO] Running in sequential loop mode.
% 1.47/11.41 % [INFO] eprover registered as external prover.
% 1.47/11.41 % [INFO] Scanning for conjecture ...
% 1.47/11.46 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 1.47/11.48 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.72/11.50 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.72/11.50 % [INFO] Type checking passed.
% 1.72/11.50 % [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 ...
% 2.67/11.83 % External prover 'e' found a proof!
% 2.67/11.83 % [INFO] Killing All external provers ...
% 2.67/11.83 % Time passed: 929ms (effective reasoning time: 607ms)
% 2.67/11.83 % 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)>
% 2.67/11.83 % Axioms used in derivation (8): axiom_2, axiom_3, axiom_1_bob, mrel_universal_#idx(b_alice), axiom_1_alice, mrel_universal_#idx(i_alice), mrel_universal_#idx(b_bob), mrel_universal_#idx(i_bob)
% 2.67/11.83 % No. of inferences in proof: 20
% 2.67/11.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 929 ms resp. 607 ms w/o parsing
% 2.67/11.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.67/11.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------