%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO891_16 : 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 09:45:38 AM UTC 2026
% Result : Theorem 3.90s 7.65s
% Output : Refutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 240 ( 2 ~; 0 |; 23 &; 177 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 55 ( 0 ^; 38 !; 17 ?; 55 :)
% 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' > $o ).
thf(qmltpeq_decl,type,
qmltpeq: '$ki_world' > $i > $i > $o ).
thf(p_decl,type,
p: '$ki_world' > $i > $o ).
thf('$ki_exists_in_world_$i_decl',type,
'$ki_exists_in_world_$i': '$ki_world' > $i > $o ).
thf(5,axiom,
! [A: '$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/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).
thf(24,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)],[5]) ).
thf(3,axiom,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(20,plain,
! [A: '$ki_world'] : ( A @ ( A @ '$ki_accessible' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ( A @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ( A @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: '$ki_world',B: '$ki_world',C: '$ki_world'] :
( ( ( C @ ( B @ '$ki_accessible' ) )
& ( B @ ( A @ '$ki_accessible' ) ) )
=> ( C @ ( A @ '$ki_accessible' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(22,plain,
! [A: '$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(1,conjecture,
( ! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [C: $i] :
( ( C @ ( A @ ( B @ qmltpeq ) ) )
& ( C @ ( B @ '$ki_exists_in_world_$i' ) ) ) ) )
=> ( ? [A: $i] :
( ? [B: '$ki_world'] :
( ( A @ ( B @ p ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) )
=> ? [A: '$ki_world'] :
( ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [C: $i] :
( ( C @ ( A @ ( B @ qmltpeq ) ) )
& ( C @ ( B @ '$ki_exists_in_world_$i' ) ) ) ) )
=> ( ? [A: $i] :
( ? [B: '$ki_world'] :
( ( A @ ( B @ p ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) )
=> ? [A: '$ki_world'] :
( ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ( ! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: '$ki_world'] :
( ( B @ ( '$ki_local_world' @ '$ki_accessible' ) )
=> ? [C: $i] :
( ( C @ ( A @ ( B @ qmltpeq ) ) )
& ( C @ ( B @ '$ki_exists_in_world_$i' ) ) ) ) )
=> ( ? [A: $i] :
( ? [B: '$ki_world'] :
( ( A @ ( B @ p ) )
& ( B @ ( '$ki_local_world' @ '$ki_accessible' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) ) )
=> ? [A: '$ki_world'] :
( ? [B: $i] :
( ( B @ ( A @ p ) )
& ( B @ ( A @ '$ki_exists_in_world_$i' ) ) )
& ( A @ ( '$ki_local_world' @ '$ki_accessible' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_nonempty') ).
thf(26,plain,
! [A: '$ki_world'] :
? [B: $i] : ( B @ ( A @ '$ki_exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: $i] :
( ( B @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ( ( B @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) )
=> ( A @ ( B @ ( '$ki_local_world' @ qmltpeq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: $i] :
( ( B @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ( ( B @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) )
=> ( A @ ( B @ ( '$ki_local_world' @ qmltpeq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: $i] :
( ( B @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [C: $i] :
( ( C @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ( ( ( C @ ( B @ ( '$ki_local_world' @ qmltpeq ) ) )
& ( B @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) ) )
=> ( C @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: $i] :
( ( B @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [C: $i] :
( ( C @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ( ( ( C @ ( B @ ( '$ki_local_world' @ qmltpeq ) ) )
& ( B @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) ) )
=> ( C @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: $i] :
( ( B @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ( ( ( A @ ( '$ki_local_world' @ p ) )
& ( B @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) ) )
=> ( B @ ( '$ki_local_world' @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p_substitution_1) ).
thf(34,plain,
! [A: $i] :
( ( A @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ! [B: $i] :
( ( B @ ( '$ki_local_world' @ '$ki_exists_in_world_$i' ) )
=> ( ( ( A @ ( '$ki_local_world' @ p ) )
& ( B @ ( A @ ( '$ki_local_world' @ qmltpeq ) ) ) )
=> ( B @ ( '$ki_local_world' @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[24,20,28,22,11,26,30,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO891_16 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.07 % 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
% 0.13/5.61 % Computer : n015.cluster.edu
% 0.13/5.61 % Model : x86_64 x86_64
% 0.13/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.61 % Memory : 8046.5625MB
% 0.13/5.61 % OS : Linux 6.8.0-71-generic
% 0.13/5.61 % CPULimit : 300
% 0.13/5.61 % WCLimit : 300
% 0.13/5.61 % DateTime : Sat Sep 26 20:18:19 UTC 2026
% 0.13/5.61 % CPUTime :
% 0.13/5.61 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
% 0.99/6.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/6.42 % [INFO] Parsing done (208ms).
% 1.46/6.43 % [INFO] Running in sequential loop mode.
% 2.07/6.85 % [INFO] eprover registered as external prover.
% 2.07/6.85 % [INFO] Scanning for conjecture ...
% 2.30/6.97 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.30/7.02 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.55/7.04 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.55/7.05 % [INFO] Type checking passed.
% 2.55/7.06 % [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 ...
% 3.90/7.65 % External prover 'e' found a proof!
% 3.90/7.65 % [INFO] Killing All external provers ...
% 3.90/7.65 % Time passed: 1890ms (effective reasoning time: 1209ms)
% 3.90/7.65 % 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)>
% 3.90/7.65 % Axioms used in derivation (8): $ki_exists_in_world_$i_nonempty, $ki_exists_in_world_$i_cumul, p_substitution_1, mrel_reflexive, reflexivity, mrel_transitive, transitivity, symmetry
% 3.90/7.65 % No. of inferences in proof: 20
% 3.90/7.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1890 ms resp. 1209 ms w/o parsing
% 4.23/7.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.23/7.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------