TSTP Solution File: SEV504^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV504^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n026.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 3.48s 1.91s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 8 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 195 ( 5 ~; 0 |; 11 &; 166 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 52 ( 0 ^ 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/sets/SUBSET\'_type',type,
'\'const/sets/SUBSET\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $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/DIFF\'_type',type,
'\'const/sets/DIFF\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $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/arith/<=\'_type',type,
'\'const/arith/<=\'': '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(sk2_type,type,
sk2: skt1 > $o ).
thf(sk3_type,type,
sk3: skt1 > '\'type/nums/num\'' ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > '\'type/nums/num\''] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/arith/<=\'' @ ( '\'const/iterate/nsum\'' @ TA @ A @ C ) @ ( '\'const/iterate/nsum\'' @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_SUBSET_SIMPLE_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > '\'type/nums/num\''] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/arith/<=\'' @ ( '\'const/iterate/nsum\'' @ TA @ A @ C ) @ ( '\'const/iterate/nsum\'' @ TA @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > '\'type/nums/num\''] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/arith/<=\'' @ ( '\'const/iterate/nsum\'' @ TA @ A @ C ) @ ( '\'const/iterate/nsum\'' @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk2,
inference(cnf,[status(esa)],[7]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/DIFF\'' @ 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_DIFF_') ).
thf(20,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/DIFF\'' @ TA @ A @ B ) )
= ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ~ ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,plain,
'\'const/sets/SUBSET\'' @ skt1 @ sk1 @ sk2,
inference(cnf,[status(esa)],[7]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ 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/SUBSET_') ).
thf(17,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ 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(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > '\'type/nums/num\''] :
( ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( '\'const/sets/FINITE\'' @ TA @ B )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ ( '\'const/sets/DIFF\'' @ TA @ A @ B ) )
=> ( ( C @ D )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) )
=> ( '\'const/arith/<=\'' @ ( '\'const/iterate/nsum\'' @ TA @ A @ C ) @ ( '\'const/iterate/nsum\'' @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_SUBSET_') ).
thf(11,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > '\'type/nums/num\''] :
( ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( '\'const/sets/FINITE\'' @ TA @ B )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ ( '\'const/sets/DIFF\'' @ TA @ A @ B ) )
=> ( ( C @ D )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ) ) )
=> ( '\'const/arith/<=\'' @ ( '\'const/iterate/nsum\'' @ TA @ A @ C ) @ ( '\'const/iterate/nsum\'' @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
~ ( '\'const/arith/<=\'' @ ( '\'const/iterate/nsum\'' @ skt1 @ sk1 @ sk3 ) @ ( '\'const/iterate/nsum\'' @ skt1 @ sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(18,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/sets/FINITE\'' @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(15,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/sets/FINITE\'' @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(47,plain,
$false,
inference(e,[status(thm)],[10,20,9,17,7,11,8,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV504^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.13 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n026.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 18:25:40 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.99 % [INFO] Parsing done (114ms).
% 1.20/1.00 % [INFO] Running in sequential loop mode.
% 1.64/1.20 % [INFO] eprover registered as external prover.
% 1.73/1.21 % [INFO] Scanning for conjecture ...
% 1.83/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.83/1.29 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.83/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.83/1.31 % [INFO] Type checking passed.
% 1.83/1.31 % [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 ...
% 3.48/1.90 % External prover 'e' found a proof!
% 3.48/1.91 % [INFO] Killing All external provers ...
% 3.48/1.91 % Time passed: 1366ms (effective reasoning time: 903ms)
% 3.48/1.91 % 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)>
% 3.48/1.91 % Axioms used in derivation (4): thm/sets/IN_DIFF_, thm/sets/SUBSET_, thm/iterate/NSUM_SUBSET_, thm/sets/FINITE_SUBSET_
% 3.48/1.91 % No. of inferences in proof: 17
% 3.48/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1366 ms resp. 903 ms w/o parsing
% 3.84/1.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.84/1.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------