%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV446^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n019.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 08:37:18 AM UTC 2026
% Result : Theorem 4.54s 2.56s
% Output : Refutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 126 ( 44 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 241 ( 18 ~; 23 |; 1 &; 199 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 57 ( 0 ^; 55 !; 0 ?; 57 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/INSERT_decl',type,
'const/sets/INSERT':
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $o ) ).
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 ).
thf(sk2_decl,type,
sk2: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1] :
~ ! [B: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ ( 'const/sets/INSERT' @ skt1 @ B @ ( 'const/sets/EMPTY' @ skt1 ) ) )
= ( A = B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1] :
( ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ A @ ( 'const/sets/EMPTY' @ skt1 ) ) )
!= ( sk1 = A ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_SING_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) ) )
= ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA,B: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ ( 'const/sets/EMPTY' @ TA ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk2 @ ( 'const/sets/EMPTY' @ skt1 ) ) )
!= ( sk1 = sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk2 @ ( 'const/sets/EMPTY' @ skt1 ) ) )
!= ( sk1 = sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(14,plain,
( ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk2 @ ( 'const/sets/EMPTY' @ skt1 ) ) )
| ( sk1 = sk2 ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(16,plain,
( ( sk2 = sk1 )
| ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk2 @ ( 'const/sets/EMPTY' @ skt1 ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) )
= ( ( A = B )
| ( 'const/sets/IN' @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_INSERT_') ).
thf(10,plain,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) )
= ( ( A = B )
| ( 'const/sets/IN' @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) )
= ( ( A = B )
| ( 'const/sets/IN' @ TA @ A @ C ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) )
= ( ( A = B )
| ( 'const/sets/IN' @ TA @ A @ C ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(55,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( sk2 = sk1 )
| ( A = B )
| ( 'const/sets/IN' @ TA @ A @ C )
| ( ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk2 @ ( 'const/sets/EMPTY' @ skt1 ) ) )
!= ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,12]) ).
thf(56,plain,
( ( sk2 = sk1 )
| ( sk1 = sk2 )
| ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( 'const/sets/EMPTY' @ skt1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(76,plain,
( ( sk2 = sk1 )
| ( sk1 = sk2 )
| ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(77,plain,
( ( sk2 = sk1 )
| ( sk2 = sk1 )
| ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(78,plain,
( ( sk2 = sk1 )
| ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(3,axiom,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).
thf(8,plain,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
inference(cnf,[status(esa)],[8]) ).
thf(80,plain,
( ( sk2 = sk1 )
| $false ),
inference(rewrite,[status(thm)],[78,9]) ).
thf(81,plain,
sk2 = sk1,
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
( ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) ) )
!= ( sk1 = sk1 ) ),
inference(rewrite,[status(thm)],[7,81]) ).
thf(83,plain,
~ ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(18,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) )
| ~ ( ( A = B )
| ( 'const/sets/IN' @ TA @ A @ C ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(25,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) )
| ( A != B ) )
& ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) )
| ~ ( 'const/sets/IN' @ TA @ A @ C ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(26,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(28,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( A != B )
| ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ B @ C ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(29,plain,
! [TA: $tType,B: TA > $o,A: TA] : ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ A @ B ) ),
inference(simp,[status(thm)],[28]) ).
thf(86,plain,
~ $true,
inference(rewrite,[status(thm)],[83,29]) ).
thf(87,plain,
$false,
inference(simp,[status(thm)],[86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV446^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.12/0.21 % Computer : n019.cluster.edu
% 0.12/0.21 % Model : x86_64 x86_64
% 0.12/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.21 % Memory : 8046.5625MB
% 0.12/0.21 % OS : Linux 6.8.0-71-generic
% 0.12/0.21 % CPULimit : 300
% 0.12/0.21 % WCLimit : 300
% 0.12/0.21 % DateTime : Tue Sep 29 15:47:18 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (187ms).
% 1.17/1.00 % [INFO] Running in sequential loop mode.
% 1.94/1.40 % [INFO] eprover registered as external prover.
% 1.94/1.40 % [INFO] Scanning for conjecture ...
% 1.94/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.08/1.53 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.08/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.54 % [INFO] Type checking passed.
% 2.08/1.55 % [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 ...
% 4.54/2.55 % [INFO] Killing All external provers ...
% 4.54/2.56 % Time passed: 2203ms (effective reasoning time: 1556ms)
% 4.54/2.56 % 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)>
% 4.54/2.56 % Axioms used in derivation (2): thm/sets/IN_INSERT_, thm/sets/NOT_IN_EMPTY_
% 4.54/2.56 % No. of inferences in proof: 30
% 4.54/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2203 ms resp. 1556 ms w/o parsing
% 4.86/2.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.86/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------