TSTP Solution File: SEV497^1 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV497^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n019.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 15:59:11 EDT 2024
% Result : Theorem 3.97s 1.97s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 12 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 290 ( 5 ~; 3 |; 7 &; 263 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 11 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 1 con; 0-6 aty)
% Number of variables : 53 ( 0 ^ 53 !; 0 ?; 53 :)
% 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/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/sets/EMPTY\'_type',type,
'\'const/sets/EMPTY\'':
!>[TA: $tType] : ( TA > $o ) ).
thf('\'const/iterate/support\'_type',type,
'\'const/iterate/support\'':
!>[TA: $tType,TB: $tType] : ( ( TB > TB > TB ) > ( TA > TB ) > ( TA > $o ) > TA > $o ) ).
thf('\'const/iterate/neutral\'_type',type,
'\'const/iterate/neutral\'':
!>[TA: $tType] : ( ( TA > TA > TA ) > TA ) ).
thf('\'const/iterate/monoidal\'_type',type,
'\'const/iterate/monoidal\'':
!>[TA: $tType] : ( ( TA > TA > TA ) > $o ) ).
thf('\'const/iterate/iterate\'_type',type,
'\'const/iterate/iterate\'':
!>[TA: $tType,TB: $tType] : ( ( TA > TA > TA ) > ( TB > $o ) > ( TB > TA ) > TA ) ).
thf('\'const/class/COND\'_type',type,
'\'const/class/COND\'':
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(skt3_type,type,
skt3: $tType ).
thf(sk1_type,type,
sk1: skt3 > skt3 > skt3 ).
thf(sk2_type,type,
sk2: skt1 > skt3 ).
thf(sk5_type,type,
sk5: skt2 > $o ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ( ! [B: TC > TA] :
( ( '\'const/iterate/iterate\'' @ TC @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TC ) @ B )
= ( '\'const/iterate/neutral\'' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( '\'const/sets/FINITE\'' @ TB @ D )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/INSERT\'' @ TB @ C @ D ) @ B )
= ( '\'const/class/COND\'' @ TA @ ( '\'const/sets/IN\'' @ TB @ C @ D ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ( ! [B: TC > TA] :
( ( '\'const/iterate/iterate\'' @ TC @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TC ) @ B )
= ( '\'const/iterate/neutral\'' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( '\'const/sets/FINITE\'' @ TB @ D )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/INSERT\'' @ TB @ C @ D ) @ B )
= ( '\'const/class/COND\'' @ TA @ ( '\'const/sets/IN\'' @ TB @ C @ D ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ( ! [B: TC > TA] :
( ( '\'const/iterate/iterate\'' @ TC @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TC ) @ B )
= ( '\'const/iterate/neutral\'' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( '\'const/sets/FINITE\'' @ TB @ D )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/INSERT\'' @ TB @ C @ D ) @ B )
= ( '\'const/class/COND\'' @ TA @ ( '\'const/sets/IN\'' @ TB @ C @ D ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( ( '\'const/iterate/iterate\'' @ skt1 @ skt3 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) @ sk2 )
!= ( '\'const/iterate/neutral\'' @ skt3 @ sk1 ) )
| ( '\'const/sets/FINITE\'' @ skt2 @ sk5 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(9,plain,
( ( ( '\'const/iterate/iterate\'' @ skt1 @ skt3 @ sk1 @ ( '\'const/sets/EMPTY\'' @ skt1 ) @ sk2 )
!= ( '\'const/iterate/neutral\'' @ skt3 @ sk1 ) )
| ( '\'const/sets/FINITE\'' @ skt2 @ sk5 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > TB,B: TA > TB,C: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ C )
=> ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/iterate/support\'' @ TB @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/FINITE_SUPPORT_') ).
thf(17,plain,
! [TA: $tType,TB: $tType,A: TB > TB > TB,B: TA > TB,C: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ C )
=> ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/iterate/support\'' @ TB @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,plain,
! [TA: $tType,TB: $tType,C: TB > $o,B: TB > TA,A: TA > TA > TA] :
( ~ ( '\'const/sets/FINITE\'' @ TB @ C )
| ( '\'const/sets/FINITE\'' @ TB @ ( '\'const/iterate/support\'' @ TA @ TB @ A @ B @ C ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ( ! [B: TB > TA] :
( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TB ) @ B )
= ( '\'const/iterate/neutral\'' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( ( '\'const/iterate/monoidal\'' @ TA @ A )
& ( '\'const/sets/FINITE\'' @ TB @ ( '\'const/iterate/support\'' @ TA @ TB @ A @ B @ D ) ) )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/INSERT\'' @ TB @ C @ D ) @ B )
= ( '\'const/class/COND\'' @ TA @ ( '\'const/sets/IN\'' @ TB @ C @ D ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_CLAUSES_GEN_') ).
thf(11,plain,
! [TA: $tType,TB: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ( ! [B: TB > TA] :
( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TB ) @ B )
= ( '\'const/iterate/neutral\'' @ TA @ A ) )
& ! [B: TB > TA,C: TB,D: TB > $o] :
( ( ( '\'const/iterate/monoidal\'' @ TA @ A )
& ( '\'const/sets/FINITE\'' @ TB @ ( '\'const/iterate/support\'' @ TA @ TB @ A @ B @ D ) ) )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/INSERT\'' @ TB @ C @ D ) @ B )
= ( '\'const/class/COND\'' @ TA @ ( '\'const/sets/IN\'' @ TB @ C @ D ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) @ ( A @ ( B @ C ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
'\'const/iterate/monoidal\'' @ skt3 @ sk1,
inference(cnf,[status(esa)],[5]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[5,9,17,18,11,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEV497^1 : TPTP v8.2.0. Released v7.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 18:49:40 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.99 % [INFO] Parsing done (112ms).
% 1.16/1.00 % [INFO] Running in sequential loop mode.
% 1.68/1.20 % [INFO] eprover registered as external prover.
% 1.77/1.21 % [INFO] Scanning for conjecture ...
% 1.90/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.90/1.30 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.90/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.32 % [INFO] Type checking passed.
% 1.90/1.32 % [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 ...
% 3.97/1.97 % External prover 'e' found a proof!
% 3.97/1.97 % [INFO] Killing All external provers ...
% 3.97/1.97 % Time passed: 1427ms (effective reasoning time: 968ms)
% 3.97/1.97 % 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)>
% 3.97/1.97 % Axioms used in derivation (2): thm/iterate/FINITE_SUPPORT_, thm/iterate/ITERATE_CLAUSES_GEN_
% 3.97/1.97 % No. of inferences in proof: 12
% 3.97/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1427 ms resp. 968 ms w/o parsing
% 4.21/2.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.21/2.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------