%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO899^8 : 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 : n018.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 2.52s 1.40s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 45 ( 4 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 59 ( 2 ~; 0 |; 3 &; 47 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 16 ( 8 ^; 5 !; 3 ?; 16 :)
% 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(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mdia_decl,type,
mdia: ( 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(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: mworld > $o,B: mworld] :
? [C: mworld] :
( ( mrel @ B @ C )
& ( A @ C ) ) ) ) ).
thf(1,conjecture,
mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mimplies @ p @ ( mbox @ q ) ) ) @ ( mimplies @ ( mbox @ p ) @ ( mdia @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( ? [A: mworld] :
( ( mrel @ mactual @ A )
& ( ( p @ A )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( q @ B ) ) ) )
=> ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( p @ A ) )
=> ? [A: mworld] :
( ( mrel @ mactual @ A )
& ( q @ A ) ) ) ),
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(14,plain,
$false,
inference(e,[status(thm)],[4,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO899^8 : 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
% 0.11/0.21 % Computer : n018.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 17:28:41 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.65/0.51 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.86/0.63 % [INFO] Parsing done (108ms).
% 1.04/0.63 % [INFO] Running in sequential loop mode.
% 1.42/0.83 % [INFO] eprover registered as external prover.
% 1.42/0.84 % [INFO] Scanning for conjecture ...
% 1.42/0.89 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.67/0.91 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.67/0.91 % [INFO] Problem is higher-order (TPTP THF).
% 1.67/0.91 % [INFO] Type checking passed.
% 1.67/0.92 % [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 ...
% 2.52/1.39 % External prover 'e' found a proof!
% 2.52/1.39 % [INFO] Killing All external provers ...
% 2.52/1.39 % Time passed: 1098ms (effective reasoning time: 758ms)
% 2.52/1.39 % 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)>
% 2.52/1.40 % Axioms used in derivation (1): mrel_reflexive
% 2.52/1.40 % No. of inferences in proof: 6
% 2.52/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1098 ms resp. 758 ms w/o parsing
% 2.80/1.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.80/1.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------