%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV459^1 : 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 : n004.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 08:37:19 AM UTC 2026
% Result : Theorem 8.04s 3.35s
% Output : Refutation 8.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 3 def)
% Number of atoms : 100 ( 20 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 219 ( 19 ~; 2 |; 8 &; 183 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 54 ( 0 ^; 51 !; 0 ?; 54 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/SUBSET_decl',type,
'const/sets/SUBSET':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('const/sets/DELETE_decl',type,
'const/sets/DELETE':
!>[TA: $tType] : ( ( TA > $o ) > TA > TA > $o ) ).
thf(sk1_decl,type,
sk1: skt1 ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk4_decl,type,
sk4: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1] :
~ ! [B: skt1 > $o] : ( 'const/sets/SUBSET' @ skt1 @ ( 'const/sets/DELETE' @ skt1 @ B @ A ) @ B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
~ ( 'const/sets/SUBSET' @ skt1 @ ( 'const/sets/DELETE' @ skt1 @ A @ sk1 ) @ A ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: skt1] :
~ ( ( 'const/sets/IN' @ skt1 @ A @ ( 'const/sets/DELETE' @ skt1 @ sk2 @ sk1 ) )
=> ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ) ) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/SUBSET' @ TA @ A @ B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
=> ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_') ).
thf(14,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/SUBSET' @ TA @ A @ B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
=> ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( 'const/sets/SUBSET' @ TA @ A @ B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
=> ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( 'const/sets/SUBSET' @ TA @ A @ B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
=> ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ ( 'const/sets/DELETE' @ TA @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/DELETE_SUBSET_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ ( 'const/sets/DELETE' @ TA @ B @ A ) @ B ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ ( 'const/sets/DELETE' @ TA @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
~ ( 'const/sets/SUBSET' @ skt1 @ ( 'const/sets/DELETE' @ skt1 @ sk2 @ sk1 ) @ sk2 ),
inference(cnf,[status(esa)],[6]) ).
thf(22,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
=> ( 'const/sets/IN' @ TA @ C @ B ) )
| ( ( 'const/sets/SUBSET' @ TA @ A @ B )
!= ( 'const/sets/SUBSET' @ skt1 @ ( 'const/sets/DELETE' @ skt1 @ sk2 @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[16,7]) ).
thf(23,plain,
~ ! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ ( 'const/sets/DELETE' @ skt1 @ sk2 @ sk1 ) )
=> ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( 'const/sets/DELETE' @ skt1 @ sk2 @ sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(40,plain,
( ( 'const/sets/IN' @ skt1 @ sk4 @ ( 'const/sets/DELETE' @ skt1 @ sk2 @ sk1 ) )
& ~ ( 'const/sets/IN' @ skt1 @ sk4 @ sk2 ) ),
inference(cnf,[status(esa)],[23]) ).
thf(41,plain,
'const/sets/IN' @ skt1 @ sk4 @ ( 'const/sets/DELETE' @ skt1 @ sk2 @ sk1 ),
inference(cnfConj,[status(thm)],[40]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/DELETE' @ TA @ A @ C ) )
= ( ( 'const/sets/IN' @ TA @ B @ A )
& ( B != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_DELETE_') ).
thf(11,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/DELETE' @ TA @ A @ C ) )
= ( ( 'const/sets/IN' @ TA @ B @ A )
& ( B != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [TA: $tType,C: TA,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/DELETE' @ TA @ A @ C ) )
= ( ( 'const/sets/IN' @ TA @ B @ A )
& ( B != C ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,C: TA,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/DELETE' @ TA @ A @ C ) )
= ( ( 'const/sets/IN' @ TA @ B @ A )
& ( B != C ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(105,plain,
! [TA: $tType,C: TA,B: TA,A: TA > $o] :
( ( ( 'const/sets/IN' @ TA @ B @ A )
& ( B != C ) )
| ( ( 'const/sets/IN' @ skt1 @ sk4 @ ( 'const/sets/DELETE' @ skt1 @ sk2 @ sk1 ) )
!= ( 'const/sets/IN' @ TA @ B @ ( 'const/sets/DELETE' @ TA @ A @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,13]) ).
thf(106,plain,
( ( 'const/sets/IN' @ skt1 @ sk4 @ sk2 )
& ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(122,plain,
( ( 'const/sets/IN' @ skt1 @ sk4 @ sk2 )
& ( sk4 != sk1 ) ),
inference(cnf,[status(esa)],[106]) ).
thf(123,plain,
'const/sets/IN' @ skt1 @ sk4 @ sk2,
inference(cnfConj,[status(thm)],[122]) ).
thf(42,plain,
~ ( 'const/sets/IN' @ skt1 @ sk4 @ sk2 ),
inference(cnfConj,[status(thm)],[40]) ).
thf(144,plain,
$false,
inference(rewrite,[status(thm)],[123,42]) ).
thf(145,plain,
$false,
inference(simp,[status(thm)],[144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV459^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.10/0.23 % Computer : n004.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 15:48:52 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.04/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.01 % [INFO] Parsing done (203ms).
% 1.22/1.03 % [INFO] Running in sequential loop mode.
% 1.98/1.43 % [INFO] eprover registered as external prover.
% 1.98/1.44 % [INFO] Scanning for conjecture ...
% 2.18/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.18/1.56 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.18/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.18/1.58 % [INFO] Type checking passed.
% 2.18/1.59 % [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 ...
% 8.04/3.34 % [INFO] Killing All external provers ...
% 8.04/3.35 % Time passed: 2966ms (effective reasoning time: 2311ms)
% 8.04/3.35 % 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)>
% 8.04/3.35 % Axioms used in derivation (2): thm/sets/SUBSET_, thm/sets/IN_DELETE_
% 8.04/3.35 % No. of inferences in proof: 23
% 8.04/3.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2966 ms resp. 2311 ms w/o parsing
% 8.52/3.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.52/3.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------