TSTP Solution File: PRO005+4 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : PRO005+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n015.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 : 600s
% DateTime : Mon Jul 18 17:53:15 EDT 2022
% Result : Theorem 0.78s 0.96s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of clauses : 54 ( 30 unt; 12 nHn; 54 RR)
% Number of literals : 98 ( 5 equ; 42 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 47 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( ~ min_precedes(X,Y,Z)
| occurrence_of('SKOLEMAAAV3'(Z,X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
cnf(11,axiom,
( ~ min_precedes(X,Y,Z)
| subactivity_occurrence(Y,'SKOLEMAAAV3'(Z,X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
cnf(12,axiom,
( ~ leaf(X,Y)
| atomic(Y)
| occurrence_of('SKOLEMAAAV4'(Y,X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
cnf(13,axiom,
( ~ leaf(X,Y)
| atomic(Y)
| leaf_occ(X,'SKOLEMAAAV4'(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
cnf(14,axiom,
( ~ occurrence_of(X,Y)
| ~ occurrence_of(X,Z)
| Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
cnf(15,axiom,
( ~ occurrence_of(X,Y)
| ~ leaf_occ(Z,X)
| ~ min_precedes(Z,U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
cnf(16,axiom,
( ~ occurrence_of(X,Y)
| ~ root_occ(Z,X)
| ~ min_precedes(U,Z,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
cnf(28,axiom,
( leaf(X,Y)
| ~ min_precedes(Z,X,Y)
| min_precedes(X,'SKOLEMAAAV8'(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_15) ).
cnf(30,axiom,
( ~ occurrence_of(X,Y)
| arboreal(X)
| ~ atomic(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_16) ).
cnf(37,axiom,
( ~ root_occ(X,Y)
| subactivity_occurrence(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_19) ).
cnf(50,axiom,
( ~ next_subocc(X,Y,Z)
| min_precedes(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_26) ).
cnf(55,axiom,
( ~ occurrence_of(X,Y)
| atomic(Y)
| ~ leaf_occ(Z,X)
| ~ leaf_occ(U,X)
| U = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_28) ).
cnf(59,axiom,
( ~ occurrence_of(X,tptp0)
| occurrence_of('SKOLEMAAAV13'(X),tptp4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
cnf(60,axiom,
( ~ occurrence_of(X,tptp0)
| root_occ('SKOLEMAAAV13'(X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
cnf(61,axiom,
( ~ occurrence_of(X,tptp0)
| occurrence_of('SKOLEMAAAV14'(X),tptp3)
| occurrence_of('SKOLEMAAAV14'(X),tptp2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
cnf(62,axiom,
( ~ occurrence_of(X,tptp0)
| leaf_occ('SKOLEMAAAV14'(X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
cnf(63,axiom,
( ~ occurrence_of(X,tptp0)
| next_subocc('SKOLEMAAAV13'(X),'SKOLEMAAAV14'(X),tptp0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).
cnf(64,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_34) ).
cnf(65,axiom,
atomic(tptp4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_35) ).
cnf(68,axiom,
atomic(tptp1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_38) ).
cnf(72,axiom,
tptp1 != tptp3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_42) ).
cnf(73,axiom,
tptp1 != tptp2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_43) ).
cnf(75,axiom,
( ~ occurrence_of(X,tptp0)
| ~ subactivity_occurrence(Y,X)
| ~ arboreal(Y)
| leaf_occ(Y,X)
| root_occ(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_45) ).
cnf(76,axiom,
( ~ occurrence_of(X,tptp0)
| ~ subactivity_occurrence(Y,X)
| ~ arboreal(Y)
| leaf_occ(Y,X)
| occurrence_of('SKOLEMAAAV15'(Y),tptp1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_46) ).
cnf(77,axiom,
( ~ occurrence_of(X,tptp0)
| ~ subactivity_occurrence(Y,X)
| ~ arboreal(Y)
| leaf_occ(Y,X)
| next_subocc(Y,'SKOLEMAAAV15'(Y),tptp0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_46) ).
cnf(78,negated_conjecture,
occurrence_of('SKOLEMAAAV16',tptp0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(81,plain,
occurrence_of('SKOLEMAAAV13'('SKOLEMAAAV16'),tptp4),
inference('HYPERRESOLVE',[status(thm)],[59,78]) ).
cnf(82,plain,
root_occ('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV16'),
inference('HYPERRESOLVE',[status(thm)],[60,78]) ).
cnf(84,plain,
next_subocc('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV14'('SKOLEMAAAV16'),tptp0),
inference('HYPERRESOLVE',[status(thm)],[63,78]) ).
cnf(98,plain,
arboreal('SKOLEMAAAV13'('SKOLEMAAAV16')),
inference('HYPERRESOLVE',[status(thm)],[30,81,65]) ).
cnf(103,plain,
subactivity_occurrence('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV16'),
inference('HYPERRESOLVE',[status(thm)],[37,82]) ).
cnf(124,plain,
( leaf_occ('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV16')
| occurrence_of('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp1) ),
inference('HYPERRESOLVE',[status(thm)],[76,103,78,98]) ).
cnf(126,plain,
( leaf_occ('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV16')
| next_subocc('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp0) ),
inference('HYPERRESOLVE',[status(thm)],[77,103,78,98]) ).
cnf(132,plain,
min_precedes('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV14'('SKOLEMAAAV16'),tptp0),
inference('HYPERRESOLVE',[status(thm)],[50,84]) ).
cnf(144,plain,
~ leaf_occ('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV16'),
inference('UR-RESOLVE',[status(thm)],[15,132,78]) ).
cnf(145,plain,
occurrence_of('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp1),
inference('REWRITE',[status(thm)],[124,144]) ).
cnf(146,plain,
next_subocc('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp0),
inference('REWRITE',[status(thm)],[126,144]) ).
cnf(170,plain,
arboreal('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16'))),
inference('HYPERRESOLVE',[status(thm)],[30,145,68]) ).
cnf(173,plain,
~ occurrence_of('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp3),
inference('UR-RESOLVE',[status(thm)],[14,145,72]) ).
cnf(174,plain,
~ occurrence_of('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp2),
inference('UR-RESOLVE',[status(thm)],[14,145,73]) ).
cnf(194,plain,
min_precedes('SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp0),
inference('HYPERRESOLVE',[status(thm)],[50,146]) ).
cnf(277,plain,
occurrence_of('SKOLEMAAAV3'(tptp0,'SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16'))),tptp0),
inference('HYPERRESOLVE',[status(thm)],[9,194]) ).
cnf(281,plain,
subactivity_occurrence('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),'SKOLEMAAAV3'(tptp0,'SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))),
inference('HYPERRESOLVE',[status(thm)],[11,194]) ).
cnf(282,plain,
( leaf('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp0)
| min_precedes('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),'SKOLEMAAAV8'('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp0),tptp0) ),
inference('HYPERRESOLVE',[status(thm)],[28,194]) ).
cnf(441,plain,
~ root_occ('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),'SKOLEMAAAV3'(tptp0,'SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))),
inference('UR-RESOLVE',[status(thm)],[16,277,194]) ).
cnf(567,plain,
leaf_occ('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),'SKOLEMAAAV3'(tptp0,'SKOLEMAAAV13'('SKOLEMAAAV16'),'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[75,281,277,170]),441]) ).
cnf(626,plain,
~ min_precedes('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),X,tptp0),
inference('UR-RESOLVE',[status(thm)],[15,567,277]) ).
cnf(627,plain,
leaf('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),tptp0),
inference('REWRITE',[status(thm)],[282,626]) ).
cnf(630,plain,
occurrence_of('SKOLEMAAAV4'(tptp0,'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16'))),tptp0),
inference('UR-RESOLVE',[status(thm)],[12,627,64]) ).
cnf(631,plain,
leaf_occ('SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),'SKOLEMAAAV4'(tptp0,'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))),
inference('UR-RESOLVE',[status(thm)],[13,627,64]) ).
cnf(646,plain,
leaf_occ('SKOLEMAAAV14'('SKOLEMAAAV4'(tptp0,'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))),'SKOLEMAAAV4'(tptp0,'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))),
inference('HYPERRESOLVE',[status(thm)],[62,630]) ).
cnf(650,plain,
( occurrence_of('SKOLEMAAAV14'('SKOLEMAAAV4'(tptp0,'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))),tptp3)
| occurrence_of('SKOLEMAAAV14'('SKOLEMAAAV4'(tptp0,'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))),tptp2) ),
inference('HYPERRESOLVE',[status(thm)],[61,630]) ).
cnf(954,plain,
'SKOLEMAAAV14'('SKOLEMAAAV4'(tptp0,'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')))) = 'SKOLEMAAAV15'('SKOLEMAAAV13'('SKOLEMAAAV16')),
inference('UR-RESOLVE',[status(thm)],[55,646,630,64,631]) ).
cnf(956,plain,
$false,
inference('REWRITE',[status(thm)],[650,174,173,954,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PRO005+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 02:49:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.46 #<PACKAGE "SNARK-USER">
% 0.20/0.46 *
% 0.20/0.46 SNARK-TPTP-OPTIONS
% 0.20/0.46 *
% 0.20/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.46 (USE-FACTORING :POS)
% 0.20/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T02:49:37
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-06-13T02:49:37
% 0.20/0.49 WARNING:
% 0.20/0.49 |activity| is a 1-ary relation that occurs only positively; disabling rows that contain it.
% 0.78/0.96
% 0.78/0.96
% 0.78/0.96 #||
% 0.78/0.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/0.96 % SZS output start Refutation
% See solution above
% 0.78/0.96 ||#
% 0.78/0.96
% 0.78/0.96 ; Summary of computation:
% 0.78/0.96 ; 3210 formulas have been input or derived (from 649 formulas).
% 0.78/0.96 ; 956 (30%) were retained. Of these,
% 0.78/0.96 ; 284 (30%) were simplified or subsumed later,
% 0.78/0.96 ; 672 (70%) are still being kept.
% 0.78/0.96 ;
% 0.78/0.96 ; Run time in seconds excluding printing time:
% 0.78/0.96 ; 0.011 2% Read assertion file (1 call)
% 0.78/0.96 ; 0.002 0% Assert (48 calls)
% 0.78/0.96 ; 0.048 10% Process new row (2,471 calls)
% 0.78/0.96 ; 0.328 67% Resolution (1,296 calls)
% 0.78/0.96 ; 0.008 2% Paramodulation (648 calls)
% 0.78/0.96 ; 0.000 0% Factoring (4 calls)
% 0.78/0.96 ; 0.003 1% Condensing (138 calls)
% 0.78/0.96 ; 0.006 1% Forward subsumption (138 calls)
% 0.78/0.96 ; 0.001 0% Backward subsumption (125 calls)
% 0.78/0.96 ; 0.000 0% Clause clause subsumption (33 calls)
% 0.78/0.96 ; 0.024 5% Forward simplification (2,286 calls)
% 0.78/0.96 ; 0.019 4% Backward simplification (956 calls)
% 0.78/0.96 ; 0.000 0% Ordering (200 calls)
% 0.78/0.96 ; 0.000 0% Sortal reasoning (32 calls)
% 0.78/0.96 ; 0.000 0% Purity testing (1 call)
% 0.78/0.96 ; 0.043 9% Other
% 0.78/0.96 ; 0.493 Total
% 0.78/0.96 ; 0.497 Real time
% 0.78/0.96 ;
% 0.78/0.96 ; Term-hash-array has 1,156 terms in all.
% 0.78/0.96 ; Feature-vector-row-index has 94 entries (98 at peak, 125 added, 31 deleted).
% 0.78/0.96 ; Feature-vector-row-index has 566 nodes (613 at peak, 966 added, 400 deleted).
% 0.78/0.96 ; Retrieved 33 possibly forward subsuming rows in 138 calls.
% 0.78/0.96 ; Retrieved 15 possibly backward subsumed rows in 125 calls.
% 0.78/0.96 ; Path-index has 834 entries (874 at peak, 1,178 added, 344 deleted).
% 0.78/0.96 ; Path-index has 4,281 nodes (4,286 at peak, 4,834 added, 553 deleted).
% 0.78/0.96 ; Trie-index has 834 entries (874 at peak, 1,178 added, 344 deleted).
% 0.78/0.96 ; Trie-index has 4,104 nodes (4,402 at peak, 6,284 added, 2,180 deleted).
% 0.78/0.96 ; Retrieved 1,319 generalization terms in 4,340 calls.
% 0.78/0.96 ; Retrieved 840 instance terms in 830 calls.
% 0.78/0.96 ; Retrieved 253,304 unifiable terms in 65,994 calls.
% 0.78/0.96 ;
% 0.78/0.96 ; The agenda of backward simplifiable rows to process has 1 entry:
% 0.78/0.96 ; 1 with value 0
% 0.78/0.96 ; The agenda of rows to process has 11 entries:
% 0.78/0.96 ; 3 with value 25 1 with value 32 1 with value 39
% 0.78/0.96 ; 2 with value 26 1 with value 33 1 with value 41
% 0.78/0.96 ; 1 with value 29 1 with value 38
% 0.78/0.96 ; The agenda of rows to give has 136 entries:
% 0.78/0.96 ; 2 with value (4 23) 5 with value (4 32) 1 with value (4 43)
% 0.78/0.96 ; 27 with value (4 24) 4 with value (4 33) 1 with value (4 44)
% 0.78/0.96 ; 21 with value (4 25) 5 with value (4 34) 2 with value (4 46)
% 0.78/0.96 ; 10 with value (4 26) 4 with value (4 36) 2 with value (4 47)
% 0.78/0.96 ; 12 with value (4 27) 3 with value (4 38) 3 with value (4 51)
% 0.78/0.96 ; 6 with value (4 28) 1 with value (4 39) 1 with value (4 52)
% 0.78/0.96 ; 10 with value (4 29) 1 with value (4 40) 1 with value (4 54)
% 0.78/0.96 ; 7 with value (4 30) 1 with value (4 41) 1 with value (4 59)
% 0.78/0.96 ; 5 with value (4 31)
% 0.78/0.96 Evaluation took:
% 0.78/0.96 0.497 seconds of real time
% 0.78/0.96 0.471108 seconds of user run time
% 0.78/0.96 0.026267 seconds of system run time
% 0.78/0.96 [Run times include 0.021 seconds GC run time.]
% 0.78/0.96 0 calls to %EVAL
% 0.78/0.96 0 page faults and
% 0.78/0.96 44,214,400 bytes consed.
% 0.78/0.96 :PROOF-FOUND
% 0.78/0.96 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T02:49:38
% 0.78/0.96 :PROOF-FOUND
% 0.78/0.96 *
%------------------------------------------------------------------------------