TSTP Solution File: SEV446^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV446^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n021.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 15:59:02 EDT 2024
% Result : Theorem 3.39s 1.83s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 74 ( 7 ~; 2 |; 0 &; 65 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 23 ( 0 ^ 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/INSERT\'_type',type,
'\'const/sets/INSERT\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $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 ).
thf(sk2_type,type,
sk2: skt1 ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_SING_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
= ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) )
= ( ( A = B )
| ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_INSERT_') ).
thf(10,plain,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) )
= ( ( A = B )
| ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(8,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(cnf,[status(esa)],[8]) ).
thf(6,plain,
( ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk2 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( sk1 = sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk2 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( sk1 = sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(30,plain,
$false,
inference(e,[status(thm)],[5,10,9,7,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV446^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n021.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 : Fri Jun 21 19:00:10 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.03 % [INFO] Parsing done (119ms).
% 1.34/1.03 % [INFO] Running in sequential loop mode.
% 1.75/1.24 % [INFO] eprover registered as external prover.
% 1.75/1.25 % [INFO] Scanning for conjecture ...
% 1.75/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.93/1.32 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.93/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.33 % [INFO] Type checking passed.
% 1.93/1.33 % [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 ...
% 3.39/1.83 % External prover 'e' found a proof!
% 3.39/1.83 % [INFO] Killing All external provers ...
% 3.39/1.83 % Time passed: 1304ms (effective reasoning time: 791ms)
% 3.39/1.83 % 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)>
% 3.39/1.83 % Axioms used in derivation (2): thm/sets/IN_INSERT_, thm/sets/NOT_IN_EMPTY_
% 3.39/1.83 % No. of inferences in proof: 11
% 3.39/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1304 ms resp. 791 ms w/o parsing
% 3.39/1.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.86 % [INFO] Killing All external provers ...
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