TSTP Solution File: SEV505^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV505^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n022.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 15:59:12 EDT 2024
% Result : Theorem 3.90s 2.34s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 14 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 192 ( 2 ~; 0 |; 10 &; 168 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-5 aty)
% Number of variables : 31 ( 0 ^ 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/sets/UNION\'_type',type,
'\'const/sets/UNION\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > 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('\'const/sets/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/nums/NUMERAL\'_type',type,
'\'const/nums/NUMERAL\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/_0\'_type',type,
'\'const/nums/_0\'': '\'type/nums/num\'' ).
thf('\'const/iterate/nsum\'_type',type,
'\'const/iterate/nsum\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > '\'type/nums/num\'' ) > '\'type/nums/num\'' ) ).
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/arith/+\'_type',type,
'\'const/arith/+\'': '\'type/nums/num\'' > '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk3_type,type,
sk3: skt1 > $o ).
thf(1,conjecture,
! [TA: $tType,A: TA > '\'type/nums/num\'',B: TA > $o,C: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/FINITE\'' @ TA @ C )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ ( '\'const/sets/INTER\'' @ TA @ B @ C ) )
=> ( ( A @ D )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) )
=> ( ( '\'const/iterate/nsum\'' @ TA @ ( '\'const/sets/UNION\'' @ TA @ B @ C ) @ A )
= ( '\'const/arith/+\'' @ ( '\'const/iterate/nsum\'' @ TA @ B @ A ) @ ( '\'const/iterate/nsum\'' @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_UNION_NONZERO_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > '\'type/nums/num\'',B: TA > $o,C: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/FINITE\'' @ TA @ C )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ ( '\'const/sets/INTER\'' @ TA @ B @ C ) )
=> ( ( A @ D )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) )
=> ( ( '\'const/iterate/nsum\'' @ TA @ ( '\'const/sets/UNION\'' @ TA @ B @ C ) @ A )
= ( '\'const/arith/+\'' @ ( '\'const/iterate/nsum\'' @ TA @ B @ A ) @ ( '\'const/iterate/nsum\'' @ TA @ C @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: TA > '\'type/nums/num\'',B: TA > $o,C: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/FINITE\'' @ TA @ C )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ ( '\'const/sets/INTER\'' @ TA @ B @ C ) )
=> ( ( A @ D )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) )
=> ( ( '\'const/iterate/nsum\'' @ TA @ ( '\'const/sets/UNION\'' @ TA @ B @ C ) @ A )
= ( '\'const/arith/+\'' @ ( '\'const/iterate/nsum\'' @ TA @ B @ A ) @ ( '\'const/iterate/nsum\'' @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk3,
inference(cnf,[status(esa)],[7]) ).
thf(3,axiom,
! [TA: $tType] :
( ( '\'const/iterate/nsum\'' @ TA )
= ( '\'const/iterate/iterate\'' @ TA @ '\'type/nums/num\'' @ '\'const/arith/+\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/nsum_') ).
thf(14,plain,
! [TA: $tType] :
( ( '\'const/iterate/nsum\'' @ TA )
= ( '\'const/iterate/iterate\'' @ TA @ '\'type/nums/num\'' @ '\'const/arith/+\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ! [B: TB > TA,C: TB > $o,D: TB > $o] :
( ( ( '\'const/sets/FINITE\'' @ TB @ C )
& ( '\'const/sets/FINITE\'' @ TB @ D )
& ! [E: TB] :
( ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) )
=> ( ( B @ E )
= ( '\'const/iterate/neutral\'' @ TA @ A ) ) ) )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/UNION\'' @ TB @ C @ D ) @ B )
= ( A @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ C @ B ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_UNION_NONZERO_') ).
thf(17,plain,
! [TA: $tType,TB: $tType,A: TA > TA > TA] :
( ( '\'const/iterate/monoidal\'' @ TA @ A )
=> ! [B: TB > TA,C: TB > $o,D: TB > $o] :
( ( ( '\'const/sets/FINITE\'' @ TB @ C )
& ( '\'const/sets/FINITE\'' @ TB @ D )
& ! [E: TB] :
( ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) )
=> ( ( B @ E )
= ( '\'const/iterate/neutral\'' @ TA @ A ) ) ) )
=> ( ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ ( '\'const/sets/UNION\'' @ TB @ C @ D ) @ B )
= ( A @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ C @ B ) @ ( '\'const/iterate/iterate\'' @ TB @ TA @ A @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
'\'const/iterate/monoidal\'' @ '\'type/nums/num\'' @ '\'const/arith/+\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_ADD_') ).
thf(22,plain,
'\'const/iterate/monoidal\'' @ '\'type/nums/num\'' @ '\'const/arith/+\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
( ( '\'const/iterate/neutral\'' @ '\'type/nums/num\'' @ '\'const/arith/+\'' )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NEUTRAL_ADD_') ).
thf(23,plain,
( ( '\'const/iterate/neutral\'' @ '\'type/nums/num\'' @ '\'const/arith/+\'' )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,plain,
$false,
inference(e,[status(thm)],[10,14,17,22,7,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV505^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.09/0.29 % Computer : n022.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri Jun 21 18:41:40 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.91/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.09 % [INFO] Parsing done (175ms).
% 1.31/1.10 % [INFO] Running in sequential loop mode.
% 1.78/1.45 % [INFO] eprover registered as external prover.
% 1.78/1.45 % [INFO] Scanning for conjecture ...
% 2.01/1.53 % [INFO] No direction of definition thm/iterate/nsum_ detected. Treating as axiom ...
% 2.06/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.06/1.60 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.06/1.60 % [INFO] No direction of definition thm/iterate/nsum_ detected. Treating as axiom ...
% 2.06/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.62 % [INFO] Type checking passed.
% 2.06/1.63 % [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 ...
% 3.90/2.33 % External prover 'e' found a proof!
% 3.90/2.33 % [INFO] Killing All external provers ...
% 3.90/2.33 % Time passed: 1875ms (effective reasoning time: 1229ms)
% 3.90/2.33 % 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)>
% 3.90/2.34 % Axioms used in derivation (4): thm/iterate/nsum_, thm/iterate/ITERATE_UNION_NONZERO_, thm/iterate/MONOIDAL_ADD_, thm/iterate/NEUTRAL_ADD_
% 3.90/2.34 % No. of inferences in proof: 13
% 3.90/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1875 ms resp. 1229 ms w/o parsing
% 4.11/2.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.11/2.39 % [INFO] Killing All external provers ...
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