%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO901^11 : TPTP v9.3.1. Released v8.1.0.
% 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 : Wed Sep 30 08:46:13 AM UTC 2026
% Result : Theorem 3.50s 2.10s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 53 ( 7 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 71 ( 2 ~; 0 |; 2 &; 58 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 22 ( 9 ^; 13 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mequiv_decl,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(p_decl,type,
p: mworld > $o ).
thf(q_decl,type,
q: mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(1,conjecture,
mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ( p @ A )
= ( q @ A ) ) )
=> ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( p @ B ) ) )
= ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( q @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(12,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ C )
& ( mrel @ A @ B ) )
=> ( mrel @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(14,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ C )
& ( mrel @ A @ B ) )
=> ( mrel @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[5,12,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO901^11 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.10/0.20 % Computer : n003.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:28:13 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.91/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.00 % [INFO] Parsing done (205ms).
% 1.26/1.01 % [INFO] Running in sequential loop mode.
% 2.15/1.42 % [INFO] eprover registered as external prover.
% 2.15/1.43 % [INFO] Scanning for conjecture ...
% 2.36/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.36/1.59 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.36/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.36/1.60 % [INFO] Type checking passed.
% 2.53/1.60 % [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 ...
% 3.50/2.10 % External prover 'e' found a proof!
% 3.50/2.10 % [INFO] Killing All external provers ...
% 3.50/2.10 % Time passed: 1754ms (effective reasoning time: 1079ms)
% 3.50/2.10 % 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)>
% 3.50/2.10 % Axioms used in derivation (2): mrel_reflexive, mrel_euclidean
% 3.50/2.10 % No. of inferences in proof: 8
% 3.50/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1754 ms resp. 1079 ms w/o parsing
% 3.75/2.15 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.75/2.15 % [INFO] Killing All external provers ...
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