TSTP Solution File: DAT280^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : DAT280^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 10:30:20 EDT 2024
% Result : Theorem 2.56s 1.49s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 11 unt; 7 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 110 ( 7 ~; 1 |; 0 &; 102 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-7 aty)
% Number of variables : 48 ( 0 ^ 44 !; 0 ?; 48 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/lists/ITLIST2\'_type',type,
'\'const/lists/ITLIST2\'':
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA > TA ) > ( '\'type/ind_types/list\'' @ TC ) > ( '\'type/ind_types/list\'' @ TB ) > TA > TA ) ).
thf('\'const/ind_types/NIL\'_type',type,
'\'const/ind_types/NIL\'':
!>[TA: $tType] : ( '\'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: skt1 > skt2 > skt3 > skt3 ).
thf(sk2_type,type,
sk2: skt3 ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: '\'type/ind_types/list\'' @ TB,C: TA] :
( ( '\'const/lists/ITLIST2\'' @ TC @ TB @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TC ) @ B @ C )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/ITLIST2_DEF_0') ).
thf(7,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: '\'type/ind_types/list\'' @ TB,C: TA] :
( ( '\'const/lists/ITLIST2\'' @ TC @ TB @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TC ) @ B @ C )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC,B: '\'type/ind_types/list\'' @ TB,A: TA > TB > TC > TC] :
( ( '\'const/lists/ITLIST2\'' @ TA @ TB @ TC @ A @ ( '\'const/ind_types/NIL\'' @ TA ) @ B @ C )
= C ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC,B: '\'type/ind_types/list\'' @ TB,A: TA > TB > TC > TC] :
( ( '\'const/lists/ITLIST2\'' @ TA @ TB @ TC @ A @ ( '\'const/ind_types/NIL\'' @ TA ) @ B @ C )
= C ),
inference(lifteq,[status(thm)],[8]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: TA] :
( ( '\'const/lists/ITLIST2\'' @ TC @ TB @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TC ) @ ( '\'const/ind_types/NIL\'' @ TB ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/ITLIST2_0') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: TA] :
( ( '\'const/lists/ITLIST2\'' @ TC @ TB @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TC ) @ ( '\'const/ind_types/NIL\'' @ TB ) @ B )
= B ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: TA] :
( ( '\'const/lists/ITLIST2\'' @ TC @ TB @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TC ) @ ( '\'const/ind_types/NIL\'' @ TB ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( '\'const/lists/ITLIST2\'' @ skt1 @ skt2 @ skt3 @ sk1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) @ ( '\'const/ind_types/NIL\'' @ skt2 ) @ sk2 )
!= sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( '\'const/lists/ITLIST2\'' @ skt1 @ skt2 @ skt3 @ sk1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) @ ( '\'const/ind_types/NIL\'' @ skt2 ) @ sk2 )
!= sk2 ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
! [TA: $tType,TB: $tType,C: skt3,B: '\'type/ind_types/list\'' @ TB,A: TA > TB > skt3 > skt3] :
( ( C != sk2 )
| ( ( '\'const/lists/ITLIST2\'' @ TA @ TB @ skt3 @ A @ ( '\'const/ind_types/NIL\'' @ TA ) @ B @ C )
!= ( '\'const/lists/ITLIST2\'' @ skt1 @ skt2 @ skt3 @ sk1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) @ ( '\'const/ind_types/NIL\'' @ skt2 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[9,6]) ).
thf(11,plain,
sk2 != sk2,
inference(pattern_uni,[status(thm)],[10:[bind(A,$thf( sk1 )),bind(B,$thf( '\'const/ind_types/NIL\'' @ skt2 )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 )),bind_type(TB,$thf( skt2 ))]]) ).
thf(12,plain,
$false,
inference(simp,[status(thm)],[11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT280^1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 18:45:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.94 % [INFO] Parsing done (104ms).
% 1.19/0.95 % [INFO] Running in sequential loop mode.
% 1.48/1.14 % [INFO] nitpick registered as external prover.
% 1.48/1.14 % [INFO] Scanning for conjecture ...
% 1.72/1.19 % [INFO] Found a conjecture and 1 axioms. Running axiom selection ...
% 1.72/1.21 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.84/1.22 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.22 % [INFO] Type checking passed.
% 1.84/1.22 % [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 ...
% 2.56/1.48 % [INFO] Killing All external provers ...
% 2.56/1.49 % Time passed: 967ms (effective reasoning time: 534ms)
% 2.56/1.49 % 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)>
% 2.56/1.49 % Axioms used in derivation (1): thm/lists/ITLIST2_DEF_0
% 2.56/1.49 % No. of inferences in proof: 12
% 2.56/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 967 ms resp. 534 ms w/o parsing
% 2.75/1.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.75/1.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------