TSTP Solution File: DAT276^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT276^1 : 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 07:39:53 EDT 2024
% Result : Theorem 8.51s 3.21s
% Output : Refutation 8.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 16
% Syntax : Number of formulae : 30 ( 18 unt; 12 typ; 0 def)
% Number of atoms : 18 ( 17 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 287 ( 4 ~; 0 |; 0 &; 283 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-6 aty)
% Number of variables : 82 ( 0 ^ 76 !; 0 ?; 82 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/lists/TL\'_type',type,
'\'const/lists/TL\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf('\'const/lists/MAP2\'_type',type,
'\'const/lists/MAP2\'':
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( '\'type/ind_types/list\'' @ TC ) > ( '\'type/ind_types/list\'' @ TB ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf('\'const/lists/HD\'_type',type,
'\'const/lists/HD\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > 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(skt2_type,type,
skt2: $tType ).
thf(skt3_type,type,
skt3: $tType ).
thf(sk1_type,type,
sk1: skt2 ).
thf(sk2_type,type,
sk2: skt3 ).
thf(sk3_type,type,
sk3: skt2 > skt3 > skt1 ).
thf(sk4_type,type,
sk4: '\'type/ind_types/list\'' @ skt2 ).
thf(sk5_type,type,
sk5: '\'type/ind_types/list\'' @ skt3 ).
thf(4,axiom,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA,B: TA] :
( ( '\'const/lists/HD\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/HD_') ).
thf(12,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA,B: TA] :
( ( '\'const/lists/HD\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [TA: $tType,B: TA,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/HD\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ A ) )
= B ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [TA: $tType,B: TA,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/HD\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ A ) )
= B ),
inference(lifteq,[status(thm)],[13]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: TB > TA > TC,D: '\'type/ind_types/list\'' @ TB,E: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ C @ ( '\'const/ind_types/CONS\'' @ TB @ A @ D ) @ ( '\'const/ind_types/CONS\'' @ TA @ B @ E ) )
= ( '\'const/ind_types/CONS\'' @ TC @ ( C @ A @ B ) @ ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MAP2_1') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: TB > TA > TC,D: '\'type/ind_types/list\'' @ TB,E: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ C @ ( '\'const/ind_types/CONS\'' @ TB @ A @ D ) @ ( '\'const/ind_types/CONS\'' @ TA @ B @ E ) )
= ( '\'const/ind_types/CONS\'' @ TC @ ( C @ A @ B ) @ ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ C @ D @ E ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: TB > TA > TC,D: '\'type/ind_types/list\'' @ TB,E: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ C @ ( '\'const/ind_types/CONS\'' @ TB @ A @ D ) @ ( '\'const/ind_types/CONS\'' @ TA @ B @ E ) )
= ( '\'const/ind_types/CONS\'' @ TC @ ( C @ A @ B ) @ ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/TL\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/TL_') ).
thf(9,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/TL\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TB > TA > TC,C: '\'type/ind_types/list\'' @ TB,D: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ B @ ( '\'const/ind_types/CONS\'' @ TB @ A @ C ) @ D )
= ( '\'const/ind_types/CONS\'' @ TC @ ( B @ A @ ( '\'const/lists/HD\'' @ TA @ D ) ) @ ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ B @ C @ ( '\'const/lists/TL\'' @ TA @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MAP2_DEF_1') ).
thf(15,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TB > TA > TC,C: '\'type/ind_types/list\'' @ TB,D: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ B @ ( '\'const/ind_types/CONS\'' @ TB @ A @ C ) @ D )
= ( '\'const/ind_types/CONS\'' @ TC @ ( B @ A @ ( '\'const/lists/HD\'' @ TA @ D ) ) @ ( '\'const/lists/MAP2\'' @ TB @ TA @ TC @ B @ C @ ( '\'const/lists/TL\'' @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: '\'type/ind_types/list\'' @ TC,C: '\'type/ind_types/list\'' @ TB,B: TB > TC > TA,A: TB] :
( ( '\'const/lists/MAP2\'' @ TB @ TC @ TA @ B @ ( '\'const/ind_types/CONS\'' @ TB @ A @ C ) @ D )
= ( '\'const/ind_types/CONS\'' @ TA @ ( B @ A @ ( '\'const/lists/HD\'' @ TC @ D ) ) @ ( '\'const/lists/MAP2\'' @ TB @ TC @ TA @ B @ C @ ( '\'const/lists/TL\'' @ TC @ D ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: '\'type/ind_types/list\'' @ TC,C: '\'type/ind_types/list\'' @ TB,B: TB > TC > TA,A: TB] :
( ( '\'const/lists/MAP2\'' @ TB @ TC @ TA @ B @ ( '\'const/ind_types/CONS\'' @ TB @ A @ C ) @ D )
= ( '\'const/ind_types/CONS\'' @ TA @ ( B @ A @ ( '\'const/lists/HD\'' @ TC @ D ) ) @ ( '\'const/lists/MAP2\'' @ TB @ TC @ TA @ B @ C @ ( '\'const/lists/TL\'' @ TC @ D ) ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(10,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/TL\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/TL\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[10]) ).
thf(7,plain,
( ( '\'const/lists/MAP2\'' @ skt2 @ skt3 @ skt1 @ sk3 @ ( '\'const/ind_types/CONS\'' @ skt2 @ sk1 @ sk4 ) @ ( '\'const/ind_types/CONS\'' @ skt3 @ sk2 @ sk5 ) )
!= ( '\'const/ind_types/CONS\'' @ skt1 @ ( sk3 @ sk1 @ sk2 ) @ ( '\'const/lists/MAP2\'' @ skt2 @ skt3 @ skt1 @ sk3 @ sk4 @ sk5 ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( '\'const/lists/MAP2\'' @ skt2 @ skt3 @ skt1 @ sk3 @ ( '\'const/ind_types/CONS\'' @ skt2 @ sk1 @ sk4 ) @ ( '\'const/ind_types/CONS\'' @ skt3 @ sk2 @ sk5 ) )
!= ( '\'const/ind_types/CONS\'' @ skt1 @ ( sk3 @ sk1 @ sk2 ) @ ( '\'const/lists/MAP2\'' @ skt2 @ skt3 @ skt1 @ sk3 @ sk4 @ sk5 ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(85,plain,
$false,
inference(e,[status(thm)],[14,6,9,17,12,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : DAT276^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n020.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 6 11:37:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.95/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.00 % [INFO] Parsing done (125ms).
% 1.29/1.01 % [INFO] Running in sequential loop mode.
% 1.64/1.20 % [INFO] eprover registered as external prover.
% 1.64/1.20 % [INFO] cvc4 registered as external prover.
% 1.64/1.20 % [INFO] Scanning for conjecture ...
% 1.84/1.26 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.96/1.29 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.96/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.96/1.30 % [INFO] Type checking passed.
% 1.96/1.30 % [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 ...
% 8.51/3.21 % External prover 'e' found a proof!
% 8.51/3.21 % [INFO] Killing All external provers ...
% 8.51/3.21 % Time passed: 2663ms (effective reasoning time: 2200ms)
% 8.51/3.21 % 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)>
% 8.51/3.21 % Axioms used in derivation (3): thm/lists/HD_, thm/lists/TL_, thm/lists/MAP2_DEF_1
% 8.51/3.21 % No. of inferences in proof: 18
% 8.51/3.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2663 ms resp. 2200 ms w/o parsing
% 8.65/3.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.65/3.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------