TSTP Solution File: DAT324^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : DAT324^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 : Mon May 20 19:48:36 EDT 2024
% Result : Theorem 3.62s 1.80s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 19 ( 3 unt; 8 typ; 0 def)
% Number of atoms : 29 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 92 ( 6 ~; 2 |; 2 &; 77 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 0 ^ 14 !; 0 ?; 19 :)
% ( 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(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(6,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk1,
inference(cnf,[status(esa)],[4]) ).
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(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(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(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 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
! [TA: $tType,A: TA > $o] :
( ( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/sets/list_of_set\'' @ TA @ A ) )
= A )
| ~ ( '\'const/sets/FINITE\'' @ TA @ A ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[6,7,11,8,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT324^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 23:09:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 1.02/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/1.01 % [INFO] Parsing done (119ms).
% 1.34/1.02 % [INFO] Running in sequential loop mode.
% 1.70/1.22 % [INFO] eprover registered as external prover.
% 1.70/1.23 % [INFO] cvc4 registered as external prover.
% 1.77/1.23 % [INFO] Scanning for conjecture ...
% 1.77/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.77/1.31 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.77/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.77/1.31 % [INFO] Type checking passed.
% 1.77/1.32 % [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 ...
% 3.62/1.79 % External prover 'e' found a proof!
% 3.62/1.79 % [INFO] Killing All external provers ...
% 3.62/1.79 % Time passed: 1286ms (effective reasoning time: 772ms)
% 3.62/1.79 % 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)>
% 3.62/1.80 % Axioms used in derivation (1): thm/sets/LIST_OF_SET_PROPERTIES_
% 3.62/1.80 % No. of inferences in proof: 11
% 3.62/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1286 ms resp. 772 ms w/o parsing
% 3.66/1.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.66/1.82 % [INFO] Killing All external provers ...
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