TSTP Solution File: DAT324^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : DAT324^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 10:30:24 EDT 2024
% Result : Theorem 3.05s 1.65s
% Output : Refutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 23 ( 4 unt; 8 typ; 0 def)
% Number of atoms : 40 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 128 ( 13 ~; 5 |; 2 &; 103 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 0 ^ 16 !; 0 ?; 21 :)
% ( 5 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/sets/set_of_list\'_type',type,
'\'const/sets/set_of_list\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > TA > $o ) ).
thf('\'const/sets/list_of_set\'_type',type,
'\'const/sets/list_of_set\'':
!>[TA: $tType] : ( ( TA > $o ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf('\'const/sets/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/sets/CARD\'_type',type,
'\'const/sets/CARD\'':
!>[TA: $tType] : ( ( TA > $o ) > '\'type/nums/num\'' ) ).
thf('\'const/lists/LENGTH\'_type',type,
'\'const/lists/LENGTH\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > '\'type/nums/num\'' ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
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/sandbox2/benchmark/theBenchmark.p','thm/sets/LIST_OF_SET_PROPERTIES_') ).
thf(8,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/lists/LENGTH\'' @ TA @ ( '\'const/sets/list_of_set\'' @ TA @ A ) )
= ( '\'const/sets/CARD\'' @ TA @ A ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(12,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)],[10]) ).
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/sandbox2/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/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(lifteq,[status(thm)],[5]) ).
thf(27,plain,
! [TA: $tType,A: TA > $o] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ A )
| ( ( '\'const/sets/CARD\'' @ TA @ A )
!= ( '\'const/sets/CARD\'' @ skt1 @ sk1 ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/sets/list_of_set\'' @ TA @ A ) )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/sets/list_of_set\'' @ skt1 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(28,plain,
( ~ ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
| ( ( '\'const/sets/CARD\'' @ skt1 @ sk1 )
!= ( '\'const/sets/CARD\'' @ skt1 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(29,plain,
~ ( '\'const/sets/FINITE\'' @ skt1 @ sk1 ),
inference(simp,[status(thm)],[28]) ).
thf(6,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk1,
inference(cnf,[status(esa)],[4]) ).
thf(30,plain,
~ $true,
inference(rewrite,[status(thm)],[29,6]) ).
thf(31,plain,
$false,
inference(simp,[status(thm)],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : DAT324^1 : TPTP v8.1.2. Released v7.0.0.
% 0.03/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 6 18:40:24 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.84/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.94 % [INFO] Parsing done (112ms).
% 1.20/0.95 % [INFO] Running in sequential loop mode.
% 1.45/1.14 % [INFO] nitpick registered as external prover.
% 1.45/1.15 % [INFO] Scanning for conjecture ...
% 1.70/1.20 % [INFO] Found a conjecture and 1 axioms. Running axiom selection ...
% 1.70/1.22 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.70/1.23 % [INFO] Problem is higher-order (TPTP THF).
% 1.70/1.23 % [INFO] Type checking passed.
% 1.85/1.23 % [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 ...
% 3.05/1.65 % [INFO] Killing All external provers ...
% 3.05/1.65 % Time passed: 1153ms (effective reasoning time: 701ms)
% 3.05/1.65 % 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)>
% 3.05/1.65 % Axioms used in derivation (1): thm/sets/LIST_OF_SET_PROPERTIES_
% 3.05/1.65 % No. of inferences in proof: 15
% 3.05/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1153 ms resp. 701 ms w/o parsing
% 3.05/1.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.05/1.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------