TSTP Solution File: SEV453^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV453^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n028.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 15:59:04 EDT 2024
% Result : Theorem 3.12s 1.97s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 78 ( 4 ~; 0 |; 2 &; 72 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-4 aty)
% Number of variables : 32 ( 0 ^ 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/UNIV\'_type',type,
'\'const/sets/UNIV\'':
!>[TA: $tType] : ( TA > $o ) ).
thf('\'const/sets/INTER\'_type',type,
'\'const/sets/INTER\'':
!>[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(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(10,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(1,conjecture,
! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INTER_UNIV_1') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INTER\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) )
!= sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIV\'' @ skt1 ) )
!= sk1 ),
inference(lifteq,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,A: TA] : ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNIV_') ).
thf(13,plain,
! [TA: $tType,A: TA] : ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,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(18,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)],[6]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ 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_INTER_') ).
thf(15,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
= ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[10,9,13,7,18,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SEV453^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.11 % Command : run_Leo-III %s %d THM
% 0.10/0.32 % Computer : n028.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 21 19:10:55 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.84/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (128ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.64/1.24 % [INFO] eprover registered as external prover.
% 1.64/1.24 % [INFO] Scanning for conjecture ...
% 1.64/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.79/1.32 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.79/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 1.79/1.34 % [INFO] Type checking passed.
% 1.79/1.34 % [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 ...
% 3.12/1.97 % External prover 'e' found a proof!
% 3.12/1.97 % [INFO] Killing All external provers ...
% 3.12/1.97 % Time passed: 1484ms (effective reasoning time: 980ms)
% 3.12/1.97 % 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)>
% 3.12/1.97 % Axioms used in derivation (4): thm/sets/IN_, thm/sets/IN_UNIV_, thm/sets/EXTENSION_, thm/sets/IN_INTER_
% 3.12/1.97 % No. of inferences in proof: 14
% 3.12/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1484 ms resp. 980 ms w/o parsing
% 3.34/2.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.34/2.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------