TSTP Solution File: SEV450^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV450^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 21 04:10:33 EDT 2024
% Result : Theorem 3.51s 1.89s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 15 unt; 5 typ; 0 def)
% Number of atoms : 50 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 79 ( 5 ~; 2 |; 0 &; 72 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 36 ( 0 ^ 34 !; 0 ?; 36 :)
% ( 2 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/UNION\'_type',type,
'\'const/sets/UNION\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(sk2_type,type,
sk2: skt1 ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/UNION\'' @ TA @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/UNION_IDEMPOT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/UNION\'' @ TA @ A @ A )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/UNION\'' @ TA @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(9,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(12,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(7,plain,
( ( '\'const/sets/UNION\'' @ skt1 @ sk1 @ sk1 )
!= sk1 ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( '\'const/sets/UNION\'' @ skt1 @ sk1 @ sk1 )
!= sk1 ),
inference(lifteq,[status(thm)],[7]) ).
thf(18,plain,
( ( '\'const/sets/UNION\'' @ skt1 @ sk1 @ sk1 @ sk2 )
!= ( sk1 @ sk2 ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(15,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)],[5]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[6,9,12,18,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV450^1 : TPTP v8.2.0. Released v7.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n015.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 19:12:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 1.01/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.01 % [INFO] Parsing done (116ms).
% 1.33/1.02 % [INFO] Running in sequential loop mode.
% 1.72/1.23 % [INFO] eprover registered as external prover.
% 1.72/1.23 % [INFO] cvc4 registered as external prover.
% 1.72/1.24 % [INFO] Scanning for conjecture ...
% 1.72/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.72/1.31 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.72/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.99/1.32 % [INFO] Type checking passed.
% 1.99/1.32 % [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 ...
% 3.51/1.89 % External prover 'e' found a proof!
% 3.51/1.89 % [INFO] Killing All external provers ...
% 3.51/1.89 % Time passed: 1370ms (effective reasoning time: 859ms)
% 3.51/1.89 % 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)>
% 3.51/1.89 % Axioms used in derivation (3): thm/sets/IN_, thm/sets/IN_UNION_, thm/sets/EXTENSION_
% 3.51/1.89 % No. of inferences in proof: 15
% 3.51/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1370 ms resp. 859 ms w/o parsing
% 3.93/1.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.93/1.92 % [INFO] Killing All external provers ...
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