TSTP Solution File: DAT319^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : DAT319^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 3.01s 1.72s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 17 unt; 6 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 222 ( 8 ~; 2 |; 0 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 0 ^ 46 !; 0 ?; 49 :)
% ( 3 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
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/NIL\'_type',type,
'\'const/ind_types/NIL\'':
!>[TA: $tType] : ( '\'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(3,axiom,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/APPEND_0') ).
thf(8,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) @ A )
= A ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) @ A )
= A ),
inference(lifteq,[status(thm)],[9]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA,C: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) @ C )
= ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/lists/APPEND\'' @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/APPEND_1') ).
thf(11,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA,C: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) @ C )
= ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/lists/APPEND\'' @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [TA: $tType,C: '\'type/ind_types/list\'' @ TA,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) @ C )
= ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/lists/APPEND\'' @ TA @ B @ C ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,C: '\'type/ind_types/list\'' @ TA,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/lists/APPEND\'' @ TA @ B @ C ) )
= ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(15,plain,
! [TB: $tType,D: '\'type/ind_types/list\'' @ TB,C: '\'type/ind_types/list\'' @ TB,B: TB,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/ind_types/CONS\'' @ TB @ B @ A )
= ( '\'const/lists/APPEND\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ B @ C ) @ D ) )
| ( ( '\'const/lists/APPEND\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) @ A )
!= ( '\'const/lists/APPEND\'' @ TB @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,13]) ).
thf(16,plain,
! [TB: $tType,B: TB,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/ind_types/CONS\'' @ TB @ B @ A )
= ( '\'const/lists/APPEND\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( '\'const/ind_types/NIL\'' @ TB )),bind(D,$thf( A ))]]) ).
thf(20,plain,
! [TA: $tType,B: TA,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/ind_types/CONS\'' @ TA @ B @ A )
= ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ ( '\'const/ind_types/NIL\'' @ TA ) ) @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) @ B )
= ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/APPEND_SING_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) @ B )
= ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/APPEND\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) @ B )
= ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( '\'const/lists/APPEND\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) @ sk2 )
!= ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ sk2 )
!= ( '\'const/lists/APPEND\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) @ sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(25,plain,
! [B: skt1,A: '\'type/ind_types/list\'' @ skt1] :
( ( ( '\'const/lists/APPEND\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) @ A )
!= ( '\'const/lists/APPEND\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) @ sk2 ) )
| ( ( '\'const/ind_types/CONS\'' @ skt1 @ B @ A )
!= ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[20,7]) ).
thf(26,plain,
( ( '\'const/lists/APPEND\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) @ sk2 )
!= ( '\'const/lists/APPEND\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ sk1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(44,plain,
$false,
inference(simp,[status(thm)],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT319^1 : TPTP v8.1.2. Released v7.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 18:45:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.97 % [INFO] Parsing done (121ms).
% 1.24/0.98 % [INFO] Running in sequential loop mode.
% 1.65/1.20 % [INFO] nitpick registered as external prover.
% 1.65/1.20 % [INFO] Scanning for conjecture ...
% 1.79/1.25 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.79/1.28 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.79/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.79/1.29 % [INFO] Type checking passed.
% 1.79/1.29 % [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 ...
% 3.01/1.71 % [INFO] Killing All external provers ...
% 3.01/1.72 % Time passed: 1198ms (effective reasoning time: 732ms)
% 3.01/1.72 % 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)>
% 3.01/1.72 % Axioms used in derivation (2): thm/lists/APPEND_0, thm/lists/APPEND_1
% 3.01/1.72 % No. of inferences in proof: 19
% 3.01/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1198 ms resp. 732 ms w/o parsing
% 3.01/1.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.01/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------