%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO887_22 : 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 : n015.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 09:45:36 AM UTC 2026
% Result : Theorem 2.65s 1.55s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 2 ~; 0 |; 13 &; 68 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 19 !; 11 ?; 30 :)
% 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' > $o ).
thf(f_decl,type,
f: '$ki_world' > $i > $o ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(3,axiom,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(13,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: '$ki_world',B: '$ki_world',C: $i] :
( ( ( A @ ( B @ '$ki_accessible' ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
=> ( C @ ( B @ '$ki_exists_in_world_$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_decr') ).
thf(17,plain,
! [A: '$ki_world',B: '$ki_world',C: $i] :
( ( ( A @ ( B @ '$ki_accessible' ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
=> ( C @ ( B @ '$ki_exists_in_world_$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ( B @ ( A @ f ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) )
=> ? [A: $i] :
( ? [B: '$ki_world'] :
( ( A @ ( B @ f ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ( B @ ( A @ f ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) )
=> ? [A: $i] :
( ? [B: '$ki_world'] :
( ( A @ ( B @ f ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ( B @ ( A @ f ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) )
=> ? [A: $i] :
( ? [B: '$ki_world'] :
( ( A @ ( B @ f ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(19,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ '$ki_accessible' ) )
& ( B @ ( A @ '$ki_accessible' ) ) )
=> ( C @ ( A @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(15,plain,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ '$ki_accessible' ) )
& ( B @ ( A @ '$ki_accessible' ) ) )
=> ( C @ ( A @ '$ki_accessible' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[13,17,7,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO887_22 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.09 % 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
% 0.15/0.40 % Computer : n015.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 20:17:43 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.95/0.80 % [INFO] Parsing done (95ms).
% 0.95/0.81 % [INFO] Running in sequential loop mode.
% 1.17/1.00 % [INFO] eprover registered as external prover.
% 1.17/1.00 % [INFO] Scanning for conjecture ...
% 1.46/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.46/1.07 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.46/1.08 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.46/1.08 % [INFO] Type checking passed.
% 1.46/1.09 % [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 ...
% 2.65/1.55 % External prover 'e' found a proof!
% 2.65/1.55 % [INFO] Killing All external provers ...
% 2.65/1.55 % Time passed: 1053ms (effective reasoning time: 733ms)
% 2.65/1.55 % 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)>
% 2.65/1.55 % Axioms used in derivation (4): mrel_reflexive, $ki_exists_in_world_$i_decr, $ki_exists_in_world_$i_nonempty, mrel_transitive
% 2.65/1.55 % No. of inferences in proof: 12
% 2.65/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1053 ms resp. 733 ms w/o parsing
% 2.65/1.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.65/1.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------