%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV489^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : Wed Sep 30 08:37:22 AM UTC 2026
% Result : Theorem 3.96s 2.20s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 31 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 60 ( 8 ~; 0 |; 1 &; 46 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 16 !; 0 ?; 18 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('const/sets/EMPTY_decl',type,
'const/sets/EMPTY':
!>[TA: $tType] : ( TA > $o ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk2_decl,type,
sk2: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ! [B: skt1] :
( ( 'const/sets/IN' @ skt1 @ B @ ( 'const/sets/EMPTY' @ skt1 ) )
=> ( A @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1] :
~ ( ( 'const/sets/IN' @ skt1 @ A @ ( 'const/sets/EMPTY' @ skt1 ) )
=> ( sk1 @ A ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] :
( ( ! [B: TA] :
( ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) )
=> ( A @ B ) ) )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FORALL_IN_CLAUSES_0') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( ! [B: TA] :
( ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) )
=> ( A @ B ) ) )
= $true ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/EMPTY' @ skt1 ) )
& ~ ( sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
'const/sets/IN' @ skt1 @ sk2 @ ( 'const/sets/EMPTY' @ skt1 ),
inference(cnfConj,[status(thm)],[6]) ).
thf(4,axiom,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).
thf(12,plain,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
$false,
inference(rewrite,[status(thm)],[7,13]) ).
thf(15,plain,
$false,
inference(simp,[status(thm)],[14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV489^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:56:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.91/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (197ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 2.06/1.40 % [INFO] eprover registered as external prover.
% 2.06/1.41 % [INFO] Scanning for conjecture ...
% 2.22/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.22/1.54 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.22/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.56 % [INFO] Type checking passed.
% 2.22/1.56 % [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 ...
% 3.71/2.19 % [INFO] Killing All external provers ...
% 3.71/2.20 % Time passed: 1857ms (effective reasoning time: 1190ms)
% 3.71/2.20 % 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)>
% 3.96/2.20 % Axioms used in derivation (1): thm/sets/NOT_IN_EMPTY_
% 3.96/2.20 % No. of inferences in proof: 10
% 3.96/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1857 ms resp. 1190 ms w/o parsing
% 3.96/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.96/2.25 % [INFO] Killing All external provers ...
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