TSTP Solution File: SEV491^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV491^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 : Tue May 21 04:10:39 EDT 2024
% Result : Theorem 18.75s 5.40s
% Output : Refutation 18.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 28 ( 7 unt; 11 typ; 0 def)
% Number of atoms : 99 ( 31 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 313 ( 13 ~; 13 |; 22 &; 250 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 2 con; 0-6 aty)
% Number of variables : 76 ( 0 ^ 68 !; 0 ?; 76 :)
% ( 8 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/HAS_SIZE\'_type',type,
'\'const/sets/HAS_SIZE\'':
!>[TA: $tType] : ( ( TA > $o ) > '\'type/nums/num\'' > $o ) ).
thf('\'const/sets/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/sets/CARD\'_type',type,
'\'const/sets/CARD\'':
!>[TA: $tType] : ( ( TA > $o ) > '\'type/nums/num\'' ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(sk2_type,type,
sk2: skt2 > $o ).
thf(sk5_type,type,
sk5:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > TB ) > ( TB > $o ) > ( TA > $o ) > $o ) ).
thf(sk6_type,type,
sk6:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > TB ) > ( TB > $o ) > ( TA > $o ) > TA ) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o,C: TB > TA,D: TA > TB] :
( ( ( ( '\'const/sets/FINITE\'' @ TB @ A )
| ( '\'const/sets/FINITE\'' @ TA @ B ) )
& ! [E: TB] :
( ( '\'const/sets/IN\'' @ TB @ E @ A )
=> ( ( '\'const/sets/IN\'' @ TA @ ( C @ E ) @ B )
& ( ( D @ ( C @ E ) )
= E ) ) )
& ! [E: TA] :
( ( '\'const/sets/IN\'' @ TA @ E @ B )
=> ( ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ A )
& ( ( C @ ( D @ E ) )
= E ) ) ) )
=> ( ( '\'const/sets/CARD\'' @ TB @ A )
= ( '\'const/sets/CARD\'' @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/BIJECTIONS_CARD_EQ_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o,C: TB > TA,D: TA > TB] :
( ( ( ( '\'const/sets/FINITE\'' @ TB @ A )
| ( '\'const/sets/FINITE\'' @ TA @ B ) )
& ! [E: TB] :
( ( '\'const/sets/IN\'' @ TB @ E @ A )
=> ( ( '\'const/sets/IN\'' @ TA @ ( C @ E ) @ B )
& ( ( D @ ( C @ E ) )
= E ) ) )
& ! [E: TA] :
( ( '\'const/sets/IN\'' @ TA @ E @ B )
=> ( ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ A )
& ( ( C @ ( D @ E ) )
= E ) ) ) )
=> ( ( '\'const/sets/CARD\'' @ TB @ A )
= ( '\'const/sets/CARD\'' @ TA @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o,C: TB > TA,D: TA > TB] :
( ( ( ( '\'const/sets/FINITE\'' @ TB @ A )
| ( '\'const/sets/FINITE\'' @ TA @ B ) )
& ! [E: TB] :
( ( '\'const/sets/IN\'' @ TB @ E @ A )
=> ( ( '\'const/sets/IN\'' @ TA @ ( C @ E ) @ B )
& ( ( D @ ( C @ E ) )
= E ) ) )
& ! [E: TA] :
( ( '\'const/sets/IN\'' @ TA @ E @ B )
=> ( ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ A )
& ( ( C @ ( D @ E ) )
= E ) ) ) )
=> ( ( '\'const/sets/CARD\'' @ TB @ A )
= ( '\'const/sets/CARD\'' @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o,C: TB > TA,D: TA > TB] :
( ( ! [E: TB] :
( ( '\'const/sets/IN\'' @ TB @ E @ A )
=> ( ( '\'const/sets/IN\'' @ TA @ ( C @ E ) @ B )
& ( ( D @ ( C @ E ) )
= E ) ) )
& ! [E: TA] :
( ( '\'const/sets/IN\'' @ TA @ E @ B )
=> ( ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ A )
& ( ( C @ ( D @ E ) )
= E ) ) ) )
=> ! [E: '\'type/nums/num\''] :
( ( '\'const/sets/HAS_SIZE\'' @ TB @ A @ E )
= ( '\'const/sets/HAS_SIZE\'' @ TA @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/BIJECTIONS_HAS_SIZE_EQ_') ).
thf(20,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o,C: TB > TA,D: TA > TB] :
( ( ! [E: TB] :
( ( '\'const/sets/IN\'' @ TB @ E @ A )
=> ( ( '\'const/sets/IN\'' @ TA @ ( C @ E ) @ B )
& ( ( D @ ( C @ E ) )
= E ) ) )
& ! [E: TA] :
( ( '\'const/sets/IN\'' @ TA @ E @ B )
=> ( ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ A )
& ( ( C @ ( D @ E ) )
= E ) ) ) )
=> ! [E: '\'type/nums/num\''] :
( ( '\'const/sets/HAS_SIZE\'' @ TB @ A @ E )
= ( '\'const/sets/HAS_SIZE\'' @ TA @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: '\'type/nums/num\''] :
( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
= ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_') ).
thf(17,plain,
! [TA: $tType,A: TA > $o,B: '\'type/nums/num\''] :
( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
= ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,plain,
( ( '\'const/sets/CARD\'' @ skt1 @ sk1 )
!= ( '\'const/sets/CARD\'' @ skt2 @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(12,plain,
( ( '\'const/sets/CARD\'' @ skt1 @ sk1 )
!= ( '\'const/sets/CARD\'' @ skt2 @ sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(8,plain,
( ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
| ( '\'const/sets/FINITE\'' @ skt2 @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(18,plain,
! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
= ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) )
= ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(41,plain,
( ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
| ( ( '\'const/sets/FINITE\'' @ skt2 @ sk2 )
!= ( '\'const/sets/FINITE\'' @ skt1 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8]) ).
thf(42,plain,
( ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
| ( ( '\'const/sets/FINITE\'' @ skt2 @ sk2 )
!= ( '\'const/sets/FINITE\'' @ skt1 @ sk1 ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(21,plain,
! [TA: $tType,TB: $tType,E: '\'type/nums/num\'',D: TB > TA,C: TA > TB,B: TB > $o,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TB @ ( C @ ( sk6 @ TB @ TA @ D @ C @ B @ A ) ) @ B )
| ( ( D @ ( C @ ( sk6 @ TB @ TA @ D @ C @ B @ A ) ) )
!= ( sk6 @ TB @ TA @ D @ C @ B @ A ) )
| ~ ( sk5 @ TB @ TA @ D @ C @ B @ A )
| ( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ E )
= ( '\'const/sets/HAS_SIZE\'' @ TB @ B @ E ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(25,plain,
! [TA: $tType,TB: $tType,E: '\'type/nums/num\'',D: TB > TA,C: TA > TB,B: TB > $o,A: TA > $o] :
( ( ( D @ ( C @ ( sk6 @ TB @ TA @ D @ C @ B @ A ) ) )
!= ( sk6 @ TB @ TA @ D @ C @ B @ A ) )
| ( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ E )
= ( '\'const/sets/HAS_SIZE\'' @ TB @ B @ E ) )
| ~ ( '\'const/sets/IN\'' @ TB @ ( C @ ( sk6 @ TB @ TA @ D @ C @ B @ A ) ) @ B )
| ~ ( sk5 @ TB @ TA @ D @ C @ B @ A ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(336,plain,
$false,
inference(e,[status(thm)],[5,20,17,12,8,19,42,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV491^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n007.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 18:45:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.00 % [INFO] Parsing done (120ms).
% 1.15/1.01 % [INFO] Running in sequential loop mode.
% 1.64/1.22 % [INFO] eprover registered as external prover.
% 1.64/1.23 % [INFO] cvc4 registered as external prover.
% 1.64/1.23 % [INFO] Scanning for conjecture ...
% 1.94/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.06/1.33 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.06/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.34 % [INFO] Type checking passed.
% 2.06/1.34 % [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 ...
% 18.75/5.39 % External prover 'e' found a proof!
% 18.75/5.39 % [INFO] Killing All external provers ...
% 18.75/5.39 % Time passed: 4855ms (effective reasoning time: 4382ms)
% 18.75/5.39 % 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)>
% 18.75/5.39 % Axioms used in derivation (2): thm/sets/BIJECTIONS_HAS_SIZE_EQ_, thm/sets/HAS_SIZE_
% 18.75/5.39 % No. of inferences in proof: 17
% 18.75/5.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4855 ms resp. 4382 ms w/o parsing
% 18.75/5.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.75/5.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------