TSTP Solution File: SEV487^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV487^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n022.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 : Mon Jun 24 16:00:23 EDT 2024
% Result : Theorem 17.96s 3.89s
% Output : Refutation 17.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 13 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 135 ( 15 ~; 1 |; 12 &; 101 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 39 ( 0 ^ 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/pairwise\'_type',type,
'\'const/sets/pairwise\'':
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > $o ) > $o ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/EMPTY\'_type',type,
'\'const/sets/EMPTY\'':
!>[TA: $tType] : ( TA > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > skt1 > $o ).
thf(sk5_type,type,
sk5: skt1 ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/pairwise_') ).
thf(9,plain,
! [TA: $tType,A: TA > $o,B: TA > TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) )
= $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/PAIRWISE_EMPTY_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) )
= $true ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > TA > $o] : ( '\'const/sets/pairwise\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(14,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ~ ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) )
| ( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
!= ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,6]) ).
thf(15,plain,
~ ! [A: skt1,B: skt1] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
& ( '\'const/sets/IN\'' @ skt1 @ B @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
& ( A != B ) )
=> ( sk1 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( '\'const/sets/EMPTY\'' @ skt1 )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(25,plain,
'\'const/sets/IN\'' @ skt1 @ sk5 @ ( '\'const/sets/EMPTY\'' @ skt1 ),
inference(cnf,[status(esa)],[15]) ).
thf(3,axiom,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).
thf(7,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(cnf,[status(esa)],[7]) ).
thf(158,plain,
$false,
inference(rewrite,[status(thm)],[25,8]) ).
thf(159,plain,
$false,
inference(simp,[status(thm)],[158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV487^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:41:40 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (101ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.63/1.17 % [INFO] nitpick registered as external prover.
% 1.63/1.18 % [INFO] Scanning for conjecture ...
% 1.73/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.81/1.24 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.81/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.81/1.25 % [INFO] Type checking passed.
% 1.81/1.26 % [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 ...
% 17.96/3.89 % [INFO] Killing All external provers ...
% 17.96/3.89 % Time passed: 3359ms (effective reasoning time: 2910ms)
% 17.96/3.89 % 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)>
% 17.96/3.89 % Axioms used in derivation (2): thm/sets/pairwise_, thm/sets/NOT_IN_EMPTY_
% 17.96/3.89 % No. of inferences in proof: 16
% 17.96/3.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3359 ms resp. 2910 ms w/o parsing
% 17.96/3.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.96/3.98 % [INFO] Killing All external provers ...
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