TSTP Solution File: SEV446^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---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 SAT
% Computer : n032.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 16:00:17 EDT 2024
% Result : Theorem 2.79s 1.61s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 205 ( 14 ~; 21 |; 0 &; 170 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 50 ( 0 ^ 50 !; 0 ?; 50 :)
% 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(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(14,plain,
( ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk2 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
| ( sk1 = sk2 ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(16,plain,
( ( sk2 = sk1 )
| ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk2 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
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(11,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) )
= ( ( A = B )
| ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) )
= ( ( A = B )
| ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(50,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( sk2 = sk1 )
| ( A = B )
| ( '\'const/sets/IN\'' @ TA @ A @ C )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk2 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,12]) ).
thf(51,plain,
( ( sk2 = sk1 )
| ( sk1 = sk2 )
| ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( '\'const/sets/EMPTY\'' @ skt1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(68,plain,
( ( sk1 = sk2 )
| ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( sk2 = sk1 ) ),
inference(cnf,[status(esa)],[51]) ).
thf(69,plain,
( ( sk2 = sk1 )
| ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(70,plain,
( ( sk2 = sk1 )
| ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[69]) ).
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(72,plain,
( ( sk2 = sk1 )
| $false ),
inference(rewrite,[status(thm)],[70,9]) ).
thf(73,plain,
sk2 = sk1,
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
( ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( sk1 = sk1 ) ),
inference(rewrite,[status(thm)],[7,73]) ).
thf(75,plain,
~ ( '\'const/sets/IN\'' @ skt1 @ sk1 @ ( '\'const/sets/INSERT\'' @ skt1 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(18,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) )
| ~ ( ( A = B )
| ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(26,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( A != B )
| ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(27,plain,
! [TA: $tType,C: TA > $o,B: TA,A: TA] :
( ( A != B )
| ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(28,plain,
! [TA: $tType,B: TA > $o,A: TA] : ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ A @ B ) ),
inference(simp,[status(thm)],[27]) ).
thf(78,plain,
~ $true,
inference(rewrite,[status(thm)],[75,28]) ).
thf(79,plain,
$false,
inference(simp,[status(thm)],[78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV446^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.09 % Command : run_Leo-III %s %d SAT
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Fri Jun 21 19:00:10 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.63/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.96/0.80 % [INFO] Parsing done (99ms).
% 0.96/0.81 % [INFO] Running in sequential loop mode.
% 1.18/1.01 % [INFO] nitpick registered as external prover.
% 1.18/1.02 % [INFO] Scanning for conjecture ...
% 1.38/1.07 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.38/1.09 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.53/1.10 % [INFO] Problem is higher-order (TPTP THF).
% 1.53/1.10 % [INFO] Type checking passed.
% 1.53/1.10 % [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 ...
% 2.56/1.61 % [INFO] Killing All external provers ...
% 2.79/1.61 % Time passed: 1191ms (effective reasoning time: 793ms)
% 2.79/1.61 % 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)>
% 2.79/1.61 % Axioms used in derivation (2): thm/sets/IN_INSERT_, thm/sets/NOT_IN_EMPTY_
% 2.79/1.61 % No. of inferences in proof: 29
% 2.79/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1191 ms resp. 793 ms w/o parsing
% 2.79/1.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.79/1.65 % [INFO] Killing All external provers ...
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