%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT324^1 : 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 : n026.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 07:48:15 AM UTC 2026
% Result : Theorem 4.47s 2.43s
% Output : Refutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 54 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 164 ( 17 ~; 7 |; 4 &; 130 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 19 ( 0 ^; 18 !; 0 ?; 19 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/nums/num_type',type,
'type/nums/num': $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/set_of_list_decl',type,
'const/sets/set_of_list':
!>[TA: $tType] : ( ( 'type/ind_types/list' @ TA ) > TA > $o ) ).
thf('const/sets/list_of_set_decl',type,
'const/sets/list_of_set':
!>[TA: $tType] : ( ( TA > $o ) > ( 'type/ind_types/list' @ TA ) ) ).
thf('const/sets/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('const/sets/CARD_decl',type,
'const/sets/CARD':
!>[TA: $tType] : ( ( TA > $o ) > 'type/nums/num' ) ).
thf('const/lists/LENGTH_decl',type,
'const/lists/LENGTH':
!>[TA: $tType] : ( ( 'type/ind_types/list' @ TA ) > 'type/nums/num' ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ( ( 'const/sets/FINITE' @ skt1 @ A )
=> ( ( 'const/lists/LENGTH' @ skt1 @ ( 'const/sets/list_of_set' @ skt1 @ A ) )
= ( 'const/sets/CARD' @ skt1 @ A ) ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( ( ( 'const/sets/set_of_list' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= A )
& ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= ( 'const/sets/CARD' @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/LIST_OF_SET_PROPERTIES_') ).
thf(9,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( ( ( 'const/sets/set_of_list' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= A )
& ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= ( 'const/sets/CARD' @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [TA: $tType,A: TA > $o] :
( ( ~ ( 'const/sets/FINITE' @ TA @ A )
| ( ( 'const/sets/set_of_list' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= A ) )
& ( ~ ( 'const/sets/FINITE' @ TA @ A )
| ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= ( 'const/sets/CARD' @ TA @ A ) ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
! [TA: $tType,A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TA @ A )
| ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= ( 'const/sets/CARD' @ TA @ A ) ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(14,plain,
! [TA: $tType,A: TA > $o] :
( ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= ( 'const/sets/CARD' @ TA @ A ) )
| ~ ( 'const/sets/FINITE' @ TA @ A ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= ( 'const/sets/CARD' @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/LENGTH_LIST_OF_SET_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= ( 'const/sets/CARD' @ TA @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,A: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
= ( 'const/sets/CARD' @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( 'const/sets/FINITE' @ skt1 @ sk1 )
& ( ( 'const/lists/LENGTH' @ skt1 @ ( 'const/sets/list_of_set' @ skt1 @ sk1 ) )
!= ( 'const/sets/CARD' @ skt1 @ sk1 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
( ( 'const/lists/LENGTH' @ skt1 @ ( 'const/sets/list_of_set' @ skt1 @ sk1 ) )
!= ( 'const/sets/CARD' @ skt1 @ sk1 ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
( ( 'const/lists/LENGTH' @ skt1 @ ( 'const/sets/list_of_set' @ skt1 @ sk1 ) )
!= ( 'const/sets/CARD' @ skt1 @ sk1 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(31,plain,
! [TA: $tType,A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TA @ A )
| ( ( 'const/sets/CARD' @ TA @ A )
!= ( 'const/sets/CARD' @ skt1 @ sk1 ) )
| ( ( 'const/lists/LENGTH' @ TA @ ( 'const/sets/list_of_set' @ TA @ A ) )
!= ( 'const/lists/LENGTH' @ skt1 @ ( 'const/sets/list_of_set' @ skt1 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,8]) ).
thf(32,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk1 )
| ( ( 'const/sets/CARD' @ skt1 @ sk1 )
!= ( 'const/sets/CARD' @ skt1 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(33,plain,
~ ( 'const/sets/FINITE' @ skt1 @ sk1 ),
inference(simp,[status(thm)],[32]) ).
thf(6,plain,
'const/sets/FINITE' @ skt1 @ sk1,
inference(cnfConj,[status(thm)],[5]) ).
thf(34,plain,
~ $true,
inference(rewrite,[status(thm)],[33,6]) ).
thf(35,plain,
$false,
inference(simp,[status(thm)],[34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT324^1 : 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
% 0.09/0.23 % Computer : n026.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 18:30:12 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 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
% 1.02/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.02 % [INFO] Parsing done (200ms).
% 1.46/1.04 % [INFO] Running in sequential loop mode.
% 2.04/1.44 % [INFO] eprover registered as external prover.
% 2.04/1.45 % [INFO] Scanning for conjecture ...
% 2.24/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.24/1.59 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.24/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.40/1.60 % [INFO] Type checking passed.
% 2.40/1.61 % [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 ...
% 4.47/2.43 % [INFO] Killing All external provers ...
% 4.47/2.43 % Time passed: 2051ms (effective reasoning time: 1384ms)
% 4.47/2.43 % 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)>
% 4.47/2.43 % Axioms used in derivation (1): thm/sets/LIST_OF_SET_PROPERTIES_
% 4.47/2.43 % No. of inferences in proof: 17
% 4.47/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2051 ms resp. 1384 ms w/o parsing
% 4.79/2.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.79/2.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------