TSTP Solution File: DAT320^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT320^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 07:39:57 EDT 2024
% Result : Theorem 3.30s 1.77s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 14 unt; 6 typ; 0 def)
% Number of atoms : 48 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 189 ( 8 ~; 4 |; 4 &; 173 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 0 ^ 37 !; 18 ?; 58 :)
% ( 3 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/lists/MEM\'_type',type,
'\'const/lists/MEM\'':
!>[TA: $tType] : ( TA > ( '\'type/ind_types/list\'' @ TA ) > $o ) ).
thf('\'const/lists/APPEND\'_type',type,
'\'const/lists/APPEND\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf('\'const/ind_types/CONS\'_type',type,
'\'const/ind_types/CONS\'':
!>[TA: $tType] : ( TA > ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 ).
thf(sk2_type,type,
sk2: '\'type/ind_types/list\'' @ skt1 ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ B )
= ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
( B
= ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ B )
= ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
( B
= ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ B )
= ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
( B
= ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ B )
= ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
( ~ ( '\'const/lists/MEM\'' @ TA @ A @ C )
& ( B
= ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_LEFT_') ).
thf(9,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ B )
= ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
( ~ ( '\'const/lists/MEM\'' @ TA @ A @ C )
& ( B
= ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA,C: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ B @ ( '\'const/ind_types/CONS\'' @ TA @ A @ C ) )
= ( ( B = A )
| ( '\'const/lists/MEM\'' @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_1') ).
thf(12,plain,
! [TA: $tType,A: TA,B: TA,C: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ B @ ( '\'const/ind_types/CONS\'' @ TA @ A @ C ) )
= ( ( B = A )
| ( '\'const/lists/MEM\'' @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ B )
= ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
( ~ ( '\'const/lists/MEM\'' @ TA @ A @ C )
& ( B
= ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ B )
= ( ? [C: '\'type/ind_types/list\'' @ TA,D: '\'type/ind_types/list\'' @ TA] :
( ~ ( '\'const/lists/MEM\'' @ TA @ A @ C )
& ( B
= ( '\'const/lists/APPEND\'' @ TA @ C @ ( '\'const/ind_types/CONS\'' @ TA @ A @ D ) ) ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(7,plain,
( ( '\'const/lists/MEM\'' @ skt1 @ sk1 @ sk2 )
!= ( ? [A: '\'type/ind_types/list\'' @ skt1,B: '\'type/ind_types/list\'' @ skt1] :
( sk2
= ( '\'const/lists/APPEND\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ B ) ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( '\'const/lists/MEM\'' @ skt1 @ sk1 @ sk2 )
!= ( ? [A: '\'type/ind_types/list\'' @ skt1,B: '\'type/ind_types/list\'' @ skt1] :
( sk2
= ( '\'const/lists/APPEND\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA,C: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ ( '\'const/lists/APPEND\'' @ TA @ B @ C ) )
= ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
| ( '\'const/lists/MEM\'' @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_') ).
thf(15,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA,C: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MEM\'' @ TA @ A @ ( '\'const/lists/APPEND\'' @ TA @ B @ C ) )
= ( ( '\'const/lists/MEM\'' @ TA @ A @ B )
| ( '\'const/lists/MEM\'' @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,plain,
$false,
inference(e,[status(thm)],[6,9,12,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT320^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n020.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 : Mon May 6 11:34:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.96 % [INFO] Parsing done (116ms).
% 1.23/0.97 % [INFO] Running in sequential loop mode.
% 1.49/1.16 % [INFO] eprover registered as external prover.
% 1.49/1.16 % [INFO] cvc4 registered as external prover.
% 1.49/1.17 % [INFO] Scanning for conjecture ...
% 1.80/1.22 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.86/1.24 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.86/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 1.86/1.26 % [INFO] Type checking passed.
% 1.86/1.26 % [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 ...
% 3.30/1.76 % External prover 'e' found a proof!
% 3.30/1.77 % [INFO] Killing All external provers ...
% 3.30/1.77 % Time passed: 1251ms (effective reasoning time: 796ms)
% 3.30/1.77 % 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)>
% 3.30/1.77 % Axioms used in derivation (3): thm/lists/MEM_APPEND_DECOMPOSE_LEFT_, thm/lists/MEM_1, thm/lists/MEM_APPEND_
% 3.30/1.77 % No. of inferences in proof: 14
% 3.30/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1251 ms resp. 796 ms w/o parsing
% 3.61/1.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.61/1.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------