%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NLP266_23 : 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 3.79s 2.42s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 0 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 272 ( 2 ~; 0 |; 33 &; 200 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 11 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 60 ( 0 ^; 40 !; 20 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf('$ki_world_type',type,
'$ki_world': $tType ).
thf('$ki_local_world_decl',type,
'$ki_local_world': '$ki_world' ).
thf('$ki_accessible_decl',type,
'$ki_accessible': '$ki_world' > '$ki_world' > $o ).
thf(u_decl,type,
u: $i ).
thf(one_decl,type,
one: $i ).
thf(number_decl,type,
number: '$ki_world' > $i > $i > $o ).
thf(string_decl,type,
string: '$ki_world' > $i > $o ).
thf(in_decl,type,
in: '$ki_world' > $i > $i > $i > $o ).
thf(do_decl,type,
do: '$ki_world' > $i > $i > $i > $o ).
thf(entry_box_decl,type,
entry_box: '$ki_world' > $i > $o ).
thf(userid_decl,type,
userid: '$ki_world' > $i > $i > $o ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(6,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ( B @ ( C @ string ) )
& ( B @ ( u @ ( C @ userid ) ) ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(24,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ( ( B @ ( C @ string ) )
& ( B @ ( u @ ( C @ userid ) ) ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ! [F: '$ki_world'] :
( ( F @ ( A @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ( G @ ( D @ ( E @ ( F @ do ) ) ) )
=> ( G @ ( C @ ( B @ ( F @ in ) ) ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( A @ '$ki_accessible' ) )
=> ( ( one @ ( C @ ( F @ number ) ) )
& ( C @ ( F @ entry_box ) )
& ( B @ ( u @ ( F @ userid ) ) ) ) )
& ( E @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( D @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ! [F: '$ki_world'] :
( ( F @ ( A @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ( G @ ( D @ ( E @ ( F @ do ) ) ) )
=> ( G @ ( C @ ( B @ ( F @ in ) ) ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( A @ '$ki_accessible' ) )
=> ( ( one @ ( C @ ( F @ number ) ) )
& ( C @ ( F @ entry_box ) )
& ( B @ ( u @ ( F @ userid ) ) ) ) )
& ( E @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( D @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ! [F: '$ki_world'] :
( ( F @ ( A @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ( G @ ( D @ ( E @ ( F @ do ) ) ) )
=> ( G @ ( C @ ( B @ ( F @ in ) ) ) ) ) ) )
& ! [F: '$ki_world'] :
( ( F @ ( A @ '$ki_accessible' ) )
=> ( ( one @ ( C @ ( F @ number ) ) )
& ( C @ ( F @ entry_box ) )
& ( B @ ( u @ ( F @ userid ) ) ) ) )
& ( E @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( D @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: $i] :
( ( C @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [D: $i] :
( ( D @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( ( ( D @ ( A @ entry_box ) )
& ( C @ ( A @ string ) ) )
=> ? [E: $i] :
( ! [F: '$ki_world'] :
( ( F @ ( A @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ( G @ ( E @ ( B @ ( F @ do ) ) ) )
=> ( G @ ( D @ ( C @ ( F @ in ) ) ) ) ) ) )
& ( E @ ( A @ '$ki_exists_in_world_$i' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(34,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: $i] :
( ( C @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [D: $i] :
( ( D @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( ( ( D @ ( A @ entry_box ) )
& ( C @ ( A @ string ) ) )
=> ? [E: $i] :
( ! [F: '$ki_world'] :
( ( F @ ( A @ '$ki_accessible' ) )
=> ! [G: $i] :
( ( G @ ( F @ '$ki_exists_in_world_$i' ) )
=> ( ( G @ ( E @ ( B @ ( F @ do ) ) ) )
=> ( G @ ( D @ ( C @ ( F @ in ) ) ) ) ) ) )
& ( E @ ( A @ '$ki_exists_in_world_$i' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(22,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(18,plain,
! [A: '$ki_world',B: '$ki_world'] : ( B @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: '$ki_world',B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).
thf(20,plain,
! [A: '$ki_world',B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ( one @ ( A @ ( B @ number ) ) )
& ( A @ ( B @ entry_box ) ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(29,plain,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ( one @ ( A @ ( B @ number ) ) )
& ( A @ ( B @ entry_box ) ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[24,9,34,22,18,20,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP266_23 : 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
% 0.16/0.41 % Computer : n016.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 01:55:44 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
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.19 % [INFO] Parsing done (201ms).
% 1.35/1.20 % [INFO] Running in sequential loop mode.
% 1.98/1.60 % [INFO] eprover registered as external prover.
% 1.98/1.61 % [INFO] Scanning for conjecture ...
% 2.17/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.17/1.78 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.35/1.80 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.35/1.81 % [INFO] Type checking passed.
% 2.35/1.82 % [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 ...
% 3.79/2.41 % External prover 'e' found a proof!
% 3.79/2.42 % [INFO] Killing All external provers ...
% 3.79/2.42 % Time passed: 1864ms (effective reasoning time: 1208ms)
% 3.79/2.42 % 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)>
% 3.79/2.42 % Axioms used in derivation (6): $ki_exists_in_world_$i_nonempty, ax1, mrel_universal, ax2, $ki_exists_in_world_$i_const, ax3
% 3.79/2.42 % No. of inferences in proof: 16
% 3.79/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1864 ms resp. 1208 ms w/o parsing
% 3.79/2.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.79/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------