%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO892_15 : 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 : n014.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 09:45:38 AM UTC 2026
% Result : Theorem 3.30s 2.30s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 2 ~; 0 |; 8 &; 56 @)
% ( 0 <=>; 11 =>; 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 : 26 ( 0 ^; 16 !; 10 ?; 26 :)
% 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 > $o ).
thf(1,conjecture,
( ? [A: '$ki_world'] :
( ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( B @ ( A @ f ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
=> ! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ? [B: '$ki_world'] :
( ( A @ ( B @ f ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ( ? [A: '$ki_world'] :
( ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( B @ ( A @ f ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
=> ! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ? [B: '$ki_world'] :
( ( A @ ( B @ f ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( ? [A: '$ki_world'] :
( ! [B: $i] :
( ( B @ ( A @ '$ki_exists_in_world_$i' ) )
=> ( B @ ( A @ f ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
=> ! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ? [B: '$ki_world'] :
( ( A @ ( B @ f ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '$ki_world'] :
? [B: '$ki_world'] : ( B @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_serial) ).
thf(13,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: '$ki_world',C: $i] :
( ( ( B @ ( A @ '$ki_accessible' ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
=> ( C @ ( B @ '$ki_exists_in_world_$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
thf(15,plain,
! [A: '$ki_world',B: '$ki_world',C: $i] :
( ( ( B @ ( A @ '$ki_accessible' ) )
& ( C @ ( A @ '$ki_exists_in_world_$i' ) ) )
=> ( C @ ( B @ '$ki_exists_in_world_$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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_$i_nonempty') ).
thf(17,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[6,13,15,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO892_15 : 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 : n014.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 20:14:32 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 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
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.19 % [INFO] Parsing done (189ms).
% 1.41/1.20 % [INFO] Running in sequential loop mode.
% 2.05/1.61 % [INFO] eprover registered as external prover.
% 2.05/1.62 % [INFO] Scanning for conjecture ...
% 2.24/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.24/1.75 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.24/1.77 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.24/1.77 % [INFO] Type checking passed.
% 2.24/1.78 % [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 ...
% 3.30/2.29 % External prover 'e' found a proof!
% 3.30/2.29 % [INFO] Killing All external provers ...
% 3.30/2.29 % Time passed: 1736ms (effective reasoning time: 1086ms)
% 3.30/2.29 % 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)>
% 3.30/2.30 % Axioms used in derivation (3): mrel_serial, $ki_exists_in_world_$i_cumul, $ki_exists_in_world_$i_nonempty
% 3.30/2.30 % No. of inferences in proof: 10
% 3.30/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1736 ms resp. 1086 ms w/o parsing
% 3.59/2.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.59/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------