%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV487^1 : 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 : n003.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 08:37:21 AM UTC 2026
% Result : Theorem 13.23s 6.03s
% Output : Refutation 13.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 81 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 185 ( 22 ~; 1 |; 19 &; 135 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 0 ^; 40 !; 0 ?; 43 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/pairwise_decl',type,
'const/sets/pairwise':
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > $o ) > $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 > skt1 > $o ).
thf(sk4_decl,type,
sk4: skt1 ).
thf(sk5_decl,type,
sk5: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > skt1 > $o] :
~ ( 'const/sets/pairwise' @ skt1 @ A @ ( 'const/sets/EMPTY' @ skt1 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: skt1] :
~ ! [B: skt1] :
( ( ( 'const/sets/IN' @ skt1 @ A @ ( 'const/sets/EMPTY' @ skt1 ) )
& ( 'const/sets/IN' @ skt1 @ B @ ( 'const/sets/EMPTY' @ skt1 ) )
& ( A != B ) )
=> ( sk1 @ A @ B ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: skt1] :
~ ( ( ( 'const/sets/IN' @ skt1 @ sk4 @ ( 'const/sets/EMPTY' @ skt1 ) )
& ( 'const/sets/IN' @ skt1 @ A @ ( 'const/sets/EMPTY' @ skt1 ) )
& ( sk4 != A ) )
=> ( sk1 @ sk4 @ A ) ) ) ) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > TA > $o] :
( ( 'const/sets/pairwise' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/pairwise_') ).
thf(9,plain,
! [TA: $tType,A: TA > $o,B: TA > TA > $o] :
( ( 'const/sets/pairwise' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ( 'const/sets/pairwise' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ( 'const/sets/pairwise' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > TA > $o] :
( ( 'const/sets/pairwise' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) )
= $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/PAIRWISE_EMPTY_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > TA > $o] :
( ( 'const/sets/pairwise' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) )
= $true ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > TA > $o] : ( 'const/sets/pairwise' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( 'const/sets/pairwise' @ skt1 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(14,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ~ ! [C: TA,D: TA] :
( ( ( 'const/sets/IN' @ TA @ C @ A )
& ( 'const/sets/IN' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) )
| ( ( 'const/sets/pairwise' @ TA @ B @ A )
!= ( 'const/sets/pairwise' @ skt1 @ sk1 @ ( 'const/sets/EMPTY' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,6]) ).
thf(15,plain,
~ ! [A: skt1,B: skt1] :
( ( ( 'const/sets/IN' @ skt1 @ A @ ( 'const/sets/EMPTY' @ skt1 ) )
& ( 'const/sets/IN' @ skt1 @ B @ ( 'const/sets/EMPTY' @ skt1 ) )
& ( A != B ) )
=> ( sk1 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( 'const/sets/EMPTY' @ skt1 )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(24,plain,
( ( 'const/sets/IN' @ skt1 @ sk4 @ ( 'const/sets/EMPTY' @ skt1 ) )
& ( 'const/sets/IN' @ skt1 @ sk5 @ ( 'const/sets/EMPTY' @ skt1 ) )
& ( sk4 != sk5 )
& ~ ( sk1 @ sk4 @ sk5 ) ),
inference(cnf,[status(esa)],[15]) ).
thf(25,plain,
'const/sets/IN' @ skt1 @ sk4 @ ( 'const/sets/EMPTY' @ skt1 ),
inference(cnfConj,[status(thm)],[24]) ).
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(7,plain,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,A: TA] :
~ ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/EMPTY' @ TA ) ),
inference(cnf,[status(esa)],[7]) ).
thf(167,plain,
$false,
inference(rewrite,[status(thm)],[25,8]) ).
thf(168,plain,
$false,
inference(simp,[status(thm)],[167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV487^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.10/0.21 % Computer : n003.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 15:54:43 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.91/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (187ms).
% 1.25/1.00 % [INFO] Running in sequential loop mode.
% 2.04/1.41 % [INFO] eprover registered as external prover.
% 2.04/1.42 % [INFO] Scanning for conjecture ...
% 2.23/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.23/1.54 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.23/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.56 % [INFO] Type checking passed.
% 2.23/1.57 % [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 ...
% 12.86/6.02 % [INFO] Killing All external provers ...
% 12.86/6.03 % Time passed: 5667ms (effective reasoning time: 5020ms)
% 12.86/6.03 % 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)>
% 13.23/6.03 % Axioms used in derivation (2): thm/sets/pairwise_, thm/sets/NOT_IN_EMPTY_
% 13.23/6.03 % No. of inferences in proof: 17
% 13.23/6.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5667 ms resp. 5020 ms w/o parsing
% 13.23/6.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.23/6.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------