%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO973_1 : TPTP v9.3.1. Released v9.1.0.
% 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 : n003.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 09:45:50 AM UTC 2026
% Result : Theorem 3.55s 2.34s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 97 ( 2 ~; 6 |; 9 &; 68 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 13 !; 13 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf('$world_type',type,
'$world': $tType ).
thf('$local_world_decl',type,
'$local_world': '$world' ).
thf('$accessible_world_decl',type,
'$accessible_world': '$world' > '$world' > $o ).
thf(p_decl,type,
p: '$world' > $i > $o ).
thf(q_decl,type,
q: '$world' > $i > $o ).
thf('$exists_in_world_$i_decl',type,
'$exists_in_world_$i': '$world' > $i > $o ).
thf(1,conjecture,
( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( ( B @ ( A @ q ) )
| ( B @ ( A @ p ) ) ) ) )
=> ( ? [A: '$world'] :
( ? [B: $i] :
( ( B @ ( A @ q ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exercise2) ).
thf(2,negated_conjecture,
~ ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( ( B @ ( A @ q ) )
| ( B @ ( A @ p ) ) ) ) )
=> ( ? [A: '$world'] :
( ? [B: $i] :
( ( B @ ( A @ q ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( ! [A: '$world'] :
( ( A @ ( '$local_world' @ '$accessible_world' ) )
=> ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( ( B @ ( A @ q ) )
| ( B @ ( A @ p ) ) ) ) )
=> ( ? [A: '$world'] :
( ? [B: $i] :
( ( B @ ( A @ q ) )
& ( B @ ( A @ '$exists_in_world_$i' ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) )
| ? [A: '$world'] :
( ! [B: $i] :
( ( B @ ( A @ '$exists_in_world_$i' ) )
=> ( B @ ( A @ p ) ) )
& ( A @ ( '$local_world' @ '$accessible_world' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '$world'] :
? [B: '$world'] : ( B @ ( A @ '$accessible_world' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_serial) ).
thf(14,plain,
! [A: '$world'] :
? [B: '$world'] : ( B @ ( A @ '$accessible_world' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: '$world'] :
? [B: $i] : ( B @ ( A @ '$exists_in_world_$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$exists_in_world_$i_nonempty') ).
thf(16,plain,
! [A: '$world'] :
? [B: $i] : ( B @ ( A @ '$exists_in_world_$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[5,14,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO973_1 : TPTP v9.3.1. Released v9.1.0.
% 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
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 20:22:10 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.87/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.16 % [INFO] Parsing done (182ms).
% 1.27/1.18 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.27/1.19 %%% First-order logic specification detected, trying modal-logic-to-TXF embedding (redirected from embedding '$$modal' to embedding '$$fomlModel' version 1.3.7) ... Use flag -p FORCE_HIGHERORDER if you want to have THF output instead.
% 1.55/1.32 % [INFO] Running in sequential loop mode.
% 2.00/1.69 % [INFO] eprover registered as external prover.
% 2.20/1.70 % [INFO] Scanning for conjecture ...
% 2.20/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.37/1.83 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.37/1.84 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.37/1.84 % [INFO] Type checking passed.
% 2.37/1.85 % [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 ...
% 3.55/2.34 % External prover 'e' found a proof!
% 3.55/2.34 % [INFO] Killing All external provers ...
% 3.55/2.34 % Time passed: 1804ms (effective reasoning time: 1016ms)
% 3.55/2.34 % 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)>
% 3.55/2.34 % Axioms used in derivation (2): mrel_serial, $exists_in_world_$i_nonempty
% 3.55/2.34 % No. of inferences in proof: 8
% 3.55/2.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1804 ms resp. 1016 ms w/o parsing
% 3.55/2.38 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.55/2.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------