%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT334_21 : 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 : n007.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 07:08:42 AM UTC 2026
% Result : Theorem 3.56s 2.43s
% Output : Refutation 3.56s
% 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 : 32 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 2 ~; 0 |; 13 &; 73 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 24 ( 0 ^; 15 !; 9 ?; 24 :)
% 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(cs_decl,type,
cs: $i ).
thf(sue_decl,type,
sue: $i ).
thf(mary_decl,type,
mary: $i ).
thf(john_decl,type,
john: $i ).
thf(math_decl,type,
math: $i ).
thf(psych_decl,type,
psych: $i ).
thf(teach_decl,type,
teach: '$ki_world' > $i > $i > $o ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(4,axiom,
! [A: '$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/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_decr') ).
thf(13,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)],[4]) ).
thf(6,axiom,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ( psych @ ( sue @ ( A @ teach ) ) )
& ( psych @ ( mary @ ( A @ teach ) ) )
& ? [B: $i] :
( ( cs @ ( B @ ( A @ teach ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( math @ ( john @ ( A @ teach ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',db) ).
thf(17,plain,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ( ( psych @ ( sue @ ( A @ teach ) ) )
& ( psych @ ( mary @ ( A @ teach ) ) )
& ? [B: $i] :
( ( cs @ ( B @ ( A @ teach ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( math @ ( john @ ( A @ teach ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ( cs @ ( B @ ( A @ teach ) ) )
& ( B @ ( A @ '$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: $i] :
( ( cs @ ( B @ ( A @ teach ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: '$ki_world'] :
( ( A @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [B: $i] :
( ( cs @ ( B @ ( A @ teach ) ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '$ki_world'] :
? [B: '$ki_world'] : ( B @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_serial) ).
thf(11,plain,
! [A: '$ki_world'] :
? [B: '$ki_world'] : ( B @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(15,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[13,17,7,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT334_21 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.07 % 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
% 0.14/0.54 % Computer : n007.cluster.edu
% 0.14/0.54 % Model : x86_64 x86_64
% 0.14/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.54 % Memory : 8046.5625MB
% 0.14/0.54 % OS : Linux 6.8.0-71-generic
% 0.14/0.54 % CPULimit : 300
% 0.14/0.54 % WCLimit : 300
% 0.14/0.54 % DateTime : Sun Sep 27 02:14:55 UTC 2026
% 0.14/0.54 % CPUTime :
% 0.14/0.54 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
% 0.88/1.12 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.31 % [INFO] Parsing done (191ms).
% 1.33/1.33 % [INFO] Running in sequential loop mode.
% 1.98/1.74 % [INFO] eprover registered as external prover.
% 1.98/1.75 % [INFO] Scanning for conjecture ...
% 2.19/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.19/1.89 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.37/1.91 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.37/1.92 % [INFO] Type checking passed.
% 2.37/1.92 % [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 ...
% 3.56/2.42 % External prover 'e' found a proof!
% 3.56/2.42 % [INFO] Killing All external provers ...
% 3.56/2.42 % Time passed: 1739ms (effective reasoning time: 1087ms)
% 3.56/2.42 % 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)>
% 3.56/2.42 % Axioms used in derivation (4): $ki_exists_in_world_$i_decr, db, mrel_serial, $ki_exists_in_world_$i_nonempty
% 3.56/2.42 % No. of inferences in proof: 12
% 3.56/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1739 ms resp. 1087 ms w/o parsing
% 3.56/2.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.56/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------