%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL953_8 : TPTP v9.3.1. Released v8.2.0.
% 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 : n006.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 07:53:27 AM UTC 2026
% Result : Theorem 4.44s 2.59s
% Output : Refutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 335 ( 11 ~; 0 |; 4 &; 235 @)
% ( 0 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 13 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 86 ( 0 ^; 80 !; 6 ?; 86 :)
% 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' > $o ).
thf(in_decl,type,
in: '$ki_world' > $i > $i > $o ).
thf(disjoint_decl,type,
disjoint: '$ki_world' > $i > $i > $o ).
thf(empty_decl,type,
empty: '$ki_world' > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( D @ ( B @ ( G @ in ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ singleton @ ( F @ disjoint ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( D @ ( B @ ( G @ in ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ singleton @ ( F @ disjoint ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( D @ ( B @ ( G @ in ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ singleton @ ( F @ disjoint ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ disjoint ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ disjoint ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(25,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ disjoint ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( B @ ( D @ ( F @ disjoint ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ in ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( B @ ( D @ ( G @ in ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(29,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ ( F @ in ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( B @ ( D @ ( G @ in ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(21,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( D @ ( B @ ( G @ in ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ singleton @ ( F @ disjoint ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(44,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ! [C: '$ki_world'] :
( ( C @ ( A @ '$ki_accessible' ) )
=> ! [D: $i] :
( ( D @ ( C @ '$ki_exists_in_world_$i' ) )
=> ! [E: '$ki_world'] :
( ( E @ ( C @ '$ki_accessible' ) )
=> ( ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ~ ! [G: '$ki_world'] :
( ( G @ ( F @ '$ki_accessible' ) )
=> ( D @ ( B @ ( G @ in ) ) ) ) )
=> ! [F: '$ki_world'] :
( ( F @ ( E @ '$ki_accessible' ) )
=> ( D @ ( B @ singleton @ ( F @ disjoint ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( A @ ( C @ empty ) ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(39,plain,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ~ ! [C: '$ki_world'] :
( ( C @ ( B @ '$ki_accessible' ) )
=> ( A @ ( C @ empty ) ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( A @ ( B @ empty ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(35,plain,
? [A: $i] :
( ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( A @ ( B @ empty ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(23,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(49,plain,
$false,
inference(e,[status(thm)],[10,25,29,21,44,39,35,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL953_8 : TPTP v9.3.1. Released v8.2.0.
% 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
% 0.14/0.42 % Computer : n006.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Fri Sep 25 23:51:10 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.86/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.22 % [INFO] Parsing done (215ms).
% 1.38/1.24 % [INFO] Running in sequential loop mode.
% 2.12/1.65 % [INFO] eprover registered as external prover.
% 2.12/1.66 % [INFO] Scanning for conjecture ...
% 2.34/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.54/1.83 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.54/1.86 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.54/1.87 % [INFO] Type checking passed.
% 2.54/1.88 % [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 ...
% 4.44/2.58 % External prover 'e' found a proof!
% 4.44/2.59 % [INFO] Killing All external provers ...
% 4.44/2.59 % Time passed: 2025ms (effective reasoning time: 1340ms)
% 4.44/2.59 % 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)>
% 4.44/2.59 % Axioms used in derivation (7): $ki_exists_in_world_$i_nonempty, mrel_reflexive, l28_zfmisc_1, rc1_xboole_0, symmetry_r1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden
% 4.44/2.59 % No. of inferences in proof: 18
% 4.44/2.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2025 ms resp. 1340 ms w/o parsing
% 4.72/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.72/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------