%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO894^8 : 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 : n001.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 08:46:12 AM UTC 2026
% Result : Theorem 2.49s 1.28s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 12 ( 10 unt; 0 typ; 6 def)
% Number of atoms : 44 ( 8 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 52 ( 5 ~; 0 |; 2 &; 41 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 13 ^; 4 !; 2 ?; 19 :)
% 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(mnot_decl,type,
mnot: ( mworld > $o ) > mworld > $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(mdia_decl,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(p_decl,type,
p: mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
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(mdia_def,definition,
( mdia
= ( ^ [A: mworld > $o,B: mworld] :
? [C: mworld] :
( ( mrel @ B @ C )
& ( A @ C ) ) ) ) ).
thf(1,conjecture,
mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mequiv @ ( mbox @ ( mimplies @ p @ ( mnot @ p ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
( ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ( p @ A )
=> ~ ( p @ A ) ) ) )
!= ( ~ ? [A: mworld] :
( ( mrel @ mactual @ A )
& ( p @ 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(6,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
$false,
inference(e,[status(thm)],[4,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO894^8 : 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
% 0.10/0.20 % Computer : n001.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 17:32:06 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.66/0.51 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.90/0.62 % [INFO] Parsing done (106ms).
% 0.90/0.62 % [INFO] Running in sequential loop mode.
% 1.43/0.82 % [INFO] eprover registered as external prover.
% 1.43/0.83 % [INFO] Scanning for conjecture ...
% 1.43/0.89 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.65/0.90 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.65/0.90 % [INFO] Problem is higher-order (TPTP THF).
% 1.65/0.91 % [INFO] Type checking passed.
% 1.65/0.91 % [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 ...
% 2.49/1.28 % External prover 'e' found a proof!
% 2.49/1.28 % [INFO] Killing All external provers ...
% 2.49/1.28 % Time passed: 990ms (effective reasoning time: 649ms)
% 2.49/1.28 % 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)>
% 2.49/1.28 % Axioms used in derivation (1): mrel_reflexive
% 2.49/1.28 % No. of inferences in proof: 6
% 2.49/1.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 990 ms resp. 649 ms w/o parsing
% 2.76/1.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.76/1.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------