TSTP Solution File: DAT326^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT326^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 3.78s 2.03s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 28 ( 19 unt; 9 typ; 0 def)
% Number of atoms : 85 ( 26 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 208 ( 5 ~; 4 |; 0 &; 199 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 58 ( 0 ^ 53 !; 0 ?; 58 :)
% ( 5 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/UNION\'_type',type,
'\'const/sets/UNION\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
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/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
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(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: '\'type/ind_types/list\'' @ skt1 ).
thf(sk2_type,type,
sk2: '\'type/ind_types/list\'' @ skt1 ).
thf(sk3_type,type,
sk3: skt1 ).
thf(3,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) )
= ( '\'const/lists/MEM\'' @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_SET_OF_LIST_') ).
thf(10,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) )
= ( '\'const/lists/MEM\'' @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(19,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(1,conjecture,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/lists/APPEND\'' @ TA @ A @ B ) )
= ( '\'const/sets/UNION\'' @ TA @ ( '\'const/sets/set_of_list\'' @ TA @ A ) @ ( '\'const/sets/set_of_list\'' @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SET_OF_LIST_APPEND_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: '\'type/ind_types/list\'' @ TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/lists/APPEND\'' @ TA @ A @ B ) )
= ( '\'const/sets/UNION\'' @ TA @ ( '\'const/sets/set_of_list\'' @ TA @ A ) @ ( '\'const/sets/set_of_list\'' @ TA @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: '\'type/ind_types/list\'' @ TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/lists/APPEND\'' @ TA @ A @ B ) )
= ( '\'const/sets/UNION\'' @ TA @ ( '\'const/sets/set_of_list\'' @ TA @ A ) @ ( '\'const/sets/set_of_list\'' @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/lists/APPEND\'' @ skt1 @ sk1 @ sk2 ) )
!= ( '\'const/sets/UNION\'' @ skt1 @ ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 ) @ ( '\'const/sets/set_of_list\'' @ skt1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/lists/APPEND\'' @ skt1 @ sk1 @ sk2 ) )
!= ( '\'const/sets/UNION\'' @ skt1 @ ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 ) @ ( '\'const/sets/set_of_list\'' @ skt1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/UNION\'' @ TA @ A @ B ) )
= ( ( '\'const/sets/IN\'' @ TA @ C @ A )
| ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(13,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/UNION\'' @ TA @ A @ B ) )
= ( ( '\'const/sets/IN\'' @ TA @ C @ A )
| ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/lists/APPEND\'' @ skt1 @ sk1 @ sk2 ) @ sk3 )
!= ( '\'const/sets/UNION\'' @ skt1 @ ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 ) @ ( '\'const/sets/set_of_list\'' @ skt1 @ sk2 ) @ sk3 ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) )
= ( '\'const/lists/MEM\'' @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) )
= ( '\'const/lists/MEM\'' @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
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(16,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(cvc4,[status(thm)],[10,21,9,13,22,12,7,16,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : DAT326^1 : TPTP v8.1.2. Released v7.0.0.
% 0.05/0.12 % Command : run_Leo-III %s %d
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon May 6 11:31:54 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.89/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (128ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 1.53/1.23 % [INFO] eprover registered as external prover.
% 1.68/1.23 % [INFO] cvc4 registered as external prover.
% 1.68/1.23 % [INFO] Scanning for conjecture ...
% 1.79/1.29 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.79/1.32 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.79/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 1.79/1.33 % [INFO] Type checking passed.
% 1.79/1.34 % [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 ...
% 3.78/2.02 % External prover 'cvc4' found a proof!
% 3.78/2.02 % [INFO] Killing All external provers ...
% 3.78/2.03 % Time passed: 1542ms (effective reasoning time: 1018ms)
% 3.78/2.03 % 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)>
% 3.78/2.03 % Axioms used in derivation (4): thm/sets/IN_SET_OF_LIST_, thm/sets/EXTENSION_, thm/sets/IN_UNION_, thm/lists/MEM_APPEND_
% 3.78/2.03 % No. of inferences in proof: 19
% 3.78/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1542 ms resp. 1018 ms w/o parsing
% 4.03/2.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.03/2.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------