TSTP Solution File: ALG251^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG251^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %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 May 20 18:05:51 EDT 2024
% Result : Theorem 0.22s 0.55s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 32
% Syntax : Number of formulae : 53 ( 13 unt; 23 typ; 0 def)
% Number of atoms : 90 ( 30 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 356 ( 23 ~; 25 |; 11 &; 244 @)
% ( 8 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 14 con; 0-4 aty)
% Number of variables : 94 ( 4 ^ 87 !; 3 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_22,type,
one: term ).
thf(decl_25,type,
sub: term > subst > term ).
thf(decl_27,type,
sh: subst ).
thf(decl_28,type,
push: term > subst > subst ).
thf(decl_29,type,
comp: subst > subst > subst ).
thf(decl_30,type,
var: term > $o ).
thf(decl_45,type,
ulamvar1: $o ).
thf(decl_71,type,
ulamvarind: $o ).
thf(decl_82,type,
axclos: $o ).
thf(decl_85,type,
pushprop_lthm: $o ).
thf(decl_92,type,
axvarcons: $o ).
thf(decl_100,type,
pushprop_lem0: $o ).
thf(decl_116,type,
pushprop: $o ).
thf(decl_136,type,
axshiftcons: $o ).
thf(decl_141,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(decl_144,type,
epred1_3: ( term > $o ) > term > subst > term > $o ).
thf(decl_145,type,
esk1_1: ( term > $o ) > term ).
thf(decl_146,type,
epred2_0: term > $o ).
thf(decl_147,type,
esk2_0: term ).
thf(decl_148,type,
esk3_0: subst ).
thf(decl_149,type,
esk4_0: term ).
thf(pushprop_lthm,axiom,
( pushprop_lthm
<=> ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop_lthm) ).
thf(pushprop_lem0,axiom,
( pushprop_lem0
<=> ! [X6: term > $o,X1: term,X3: subst] :
? [X9: term > $o] : ( pushprop_p_and_p_prime @ X1 @ X3 @ X6 @ X9 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop_lem0) ).
thf(ulamvar1,axiom,
( ulamvar1
<=> ( var @ one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvar1) ).
thf(axvarcons,axiom,
( axvarcons
<=> ! [X1: term,X3: subst] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarcons) ).
thf(axclos,axiom,
( axclos
<=> ! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axclos) ).
thf(axshiftcons,axiom,
( axshiftcons
<=> ! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axshiftcons) ).
thf(ulamvarind,axiom,
( ulamvarind
<=> ! [X6: term > $o] :
( ( X6 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X6 @ X1 )
=> ( X6 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X6 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvarind) ).
thf(pushprop,axiom,
( pushprop
<=> ! [X6: term > $o,X1: term,X3: subst] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ X3 ) ) )
=> ( ( X6 @ X1 )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ ( push @ X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop) ).
thf(thm,conjecture,
pushprop_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(c_0_9,axiom,
( pushprop_lthm
= ( ! [X47: term > $o,X48: term,X49: subst] :
? [X50: term > $o] : ( pushprop_p_and_p_prime @ X48 @ X49 @ X47 @ X50 )
=> ( ( var @ one )
=> ( ! [X51: term,X52: subst] :
( ( sub @ one @ ( push @ X51 @ X52 ) )
= X51 )
=> ( ! [X53: term,X54: subst,X55: subst] :
( ( sub @ ( sub @ X53 @ X54 ) @ X55 )
= ( sub @ X53 @ ( comp @ X54 @ X55 ) ) )
=> ( ! [X56: term,X57: subst] :
( ( comp @ sh @ ( push @ X56 @ X57 ) )
= X57 )
=> ( ! [X58: term > $o] :
( ( X58 @ one )
=> ( ! [X59: term] :
( ( var @ X59 )
=> ( ( X58 @ X59 )
=> ( X58 @ ( sub @ X59 @ sh ) ) ) )
=> ! [X60: term] :
( ( var @ X60 )
=> ( X58 @ X60 ) ) ) )
=> ! [X61: term > $o,X62: term,X63: subst] :
( ! [X64: term] :
( ( var @ X64 )
=> ( X61 @ ( sub @ X64 @ X63 ) ) )
=> ( ( X61 @ X62 )
=> ! [X65: term] :
( ( var @ X65 )
=> ( X61 @ ( sub @ X65 @ ( push @ X62 @ X63 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[pushprop_lthm,pushprop_lem0]),ulamvar1]),axvarcons]),axclos]),axshiftcons]),ulamvarind]),pushprop]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X66: term > $o,X67: term,X68: subst] :
? [X69: term > $o] : ( pushprop_p_and_p_prime @ X67 @ X68 @ X66 @ X69 )
=> ( ( var @ one )
=> ( ! [X70: term,X71: subst] :
( ( sub @ one @ ( push @ X70 @ X71 ) )
= X70 )
=> ( ! [X72: term,X73: subst,X74: subst] :
( ( sub @ ( sub @ X72 @ X73 ) @ X74 )
= ( sub @ X72 @ ( comp @ X73 @ X74 ) ) )
=> ( ! [X75: term,X76: subst] :
( ( comp @ sh @ ( push @ X75 @ X76 ) )
= X76 )
=> ( ! [X77: term > $o] :
( ( X77 @ one )
=> ( ! [X78: term] :
( ( var @ X78 )
=> ( ( X77 @ X78 )
=> ( X77 @ ( sub @ X78 @ sh ) ) ) )
=> ! [X79: term] :
( ( var @ X79 )
=> ( X77 @ X79 ) ) ) )
=> ! [X80: term > $o,X81: term,X82: subst] :
( ! [X83: term] :
( ( var @ X83 )
=> ( X80 @ ( sub @ X83 @ X82 ) ) )
=> ( ( X80 @ X81 )
=> ! [X84: term] :
( ( var @ X84 )
=> ( X80 @ ( sub @ X84 @ ( push @ X81 @ X82 ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X85: term > $o,X86: term,X87: subst,X89: term,X90: subst,X91: term,X92: subst,X93: subst,X94: term,X95: subst,X96: term > $o,X98: term,X102: term] :
( ( pushprop_p_and_p_prime @ X86 @ X87 @ X85 @ ( epred1_3 @ X85 @ X86 @ X87 ) )
& ( var @ one )
& ( ( sub @ one @ ( push @ X89 @ X90 ) )
= X89 )
& ( ( sub @ ( sub @ X91 @ X92 ) @ X93 )
= ( sub @ X91 @ ( comp @ X92 @ X93 ) ) )
& ( ( comp @ sh @ ( push @ X94 @ X95 ) )
= X95 )
& ( ( var @ ( esk1_1 @ X96 ) )
| ~ ( var @ X98 )
| ( X96 @ X98 )
| ~ ( X96 @ one ) )
& ( ( X96 @ ( esk1_1 @ X96 ) )
| ~ ( var @ X98 )
| ( X96 @ X98 )
| ~ ( X96 @ one ) )
& ( ~ ( X96 @ ( sub @ ( esk1_1 @ X96 ) @ sh ) )
| ~ ( var @ X98 )
| ( X96 @ X98 )
| ~ ( X96 @ one ) )
& ( ~ ( var @ X102 )
| ( epred2_0 @ ( sub @ X102 @ esk3_0 ) ) )
& ( epred2_0 @ esk2_0 )
& ( var @ esk4_0 )
& ~ ( epred2_0 @ ( sub @ esk4_0 @ ( push @ esk2_0 @ esk3_0 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])]) ).
thf(c_0_12,negated_conjecture,
! [X1: term,X6: term > $o] :
( ( X6 @ X1 )
| ~ ( X6 @ ( sub @ ( esk1_1 @ X6 ) @ sh ) )
| ~ ( var @ X1 )
| ~ ( X6 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: term] :
( ( ( sub
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != X1 ) )
@ sh )
= X1 )
| ( one = X1 )
| ~ ( var @ X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
var @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,negated_conjecture,
! [X1: term,X6: term > $o] :
( ( var @ ( esk1_1 @ X6 ) )
| ( X6 @ X1 )
| ~ ( var @ X1 )
| ~ ( X6 @ one ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
! [X1: term,X2: term,X3: subst] :
( ( sub @ ( sub @ X1 @ sh ) @ ( push @ X2 @ X3 ) )
= ( sub @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_19,negated_conjecture,
( ( ( sub
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != esk4_0 ) )
@ sh )
= esk4_0 )
| ( esk4_0 = one ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X6: term > $o] :
( ( var @ ( esk1_1 @ X6 ) )
| ( X6 @ esk4_0 )
| ~ ( X6 @ one ) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
thf(c_0_21,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ ( sub @ X1 @ esk3_0 ) )
| ~ ( var @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_22,negated_conjecture,
! [X1: term,X3: subst] :
( ( ( sub @ esk4_0 @ ( push @ X1 @ X3 ) )
= ( sub
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != esk4_0 ) )
@ X3 ) )
| ( esk4_0 = one ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_23,negated_conjecture,
( ( esk4_0 = one )
| ( var
@ ( esk1_1
@ ^ [Z0: term] : ( Z0 != esk4_0 ) ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_20]) ).
thf(c_0_24,negated_conjecture,
~ ( epred2_0 @ ( sub @ esk4_0 @ ( push @ esk2_0 @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_25,negated_conjecture,
! [X1: term] :
( ( esk4_0 = one )
| ( epred2_0 @ ( sub @ esk4_0 @ ( push @ X1 @ esk3_0 ) ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_26,negated_conjecture,
esk4_0 = one,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_27,negated_conjecture,
! [X3: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_28,negated_conjecture,
epred2_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_26]),c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG251^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 23:09:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.48 Running higher-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.55 # Version: 3.1.0-ho
% 0.22/0.55 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.55 # Starting post_as_ho1 with 300s (1) cores
% 0.22/0.55 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.55 # Starting post_as_ho10 with 300s (1) cores
% 0.22/0.55 # post_as_ho5 with pid 19059 completed with status 0
% 0.22/0.55 # Result found by post_as_ho5
% 0.22/0.55 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.55 # Starting post_as_ho1 with 300s (1) cores
% 0.22/0.55 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.55 # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.55 # Search class: HGUSM-FFSS21-SHFMMSBN
% 0.22/0.55 # partial match(2): HGUSM-FFSS32-SHFMMSBN
% 0.22/0.55 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.55 # Starting ho_unfolding_3 with 163s (1) cores
% 0.22/0.55 # ho_unfolding_3 with pid 19061 completed with status 0
% 0.22/0.55 # Result found by ho_unfolding_3
% 0.22/0.55 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.55 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.55 # Starting post_as_ho1 with 300s (1) cores
% 0.22/0.55 # Starting post_as_ho5 with 300s (1) cores
% 0.22/0.55 # SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.22/0.55 # Search class: HGUSM-FFSS21-SHFMMSBN
% 0.22/0.55 # partial match(2): HGUSM-FFSS32-SHFMMSBN
% 0.22/0.55 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.55 # Starting ho_unfolding_3 with 163s (1) cores
% 0.22/0.55 # Preprocessing time : 0.002 s
% 0.22/0.55 # Presaturation interreduction done
% 0.22/0.55
% 0.22/0.55 # Proof found!
% 0.22/0.55 # SZS status Theorem
% 0.22/0.55 # SZS output start CNFRefutation
% See solution above
% 0.22/0.55 # Parsed axioms : 238
% 0.22/0.55 # Removed by relevancy pruning/SinE : 229
% 0.22/0.55 # Initial clauses : 12
% 0.22/0.55 # Removed in clause preprocessing : 0
% 0.22/0.55 # Initial clauses in saturation : 12
% 0.22/0.55 # Processed clauses : 198
% 0.22/0.55 # ...of these trivial : 3
% 0.22/0.55 # ...subsumed : 96
% 0.22/0.55 # ...remaining for further processing : 99
% 0.22/0.55 # Other redundant clauses eliminated : 1
% 0.22/0.55 # Clauses deleted for lack of memory : 0
% 0.22/0.55 # Backward-subsumed : 1
% 0.22/0.55 # Backward-rewritten : 39
% 0.22/0.55 # Generated clauses : 656
% 0.22/0.55 # ...of the previous two non-redundant : 643
% 0.22/0.55 # ...aggressively subsumed : 0
% 0.22/0.55 # Contextual simplify-reflections : 1
% 0.22/0.55 # Paramodulations : 628
% 0.22/0.55 # Factorizations : 0
% 0.22/0.55 # NegExts : 3
% 0.22/0.55 # Equation resolutions : 2
% 0.22/0.55 # Disequality decompositions : 0
% 0.22/0.55 # Total rewrite steps : 238
% 0.22/0.55 # ...of those cached : 161
% 0.22/0.55 # Propositional unsat checks : 0
% 0.22/0.55 # Propositional check models : 0
% 0.22/0.55 # Propositional check unsatisfiable : 0
% 0.22/0.55 # Propositional clauses : 0
% 0.22/0.55 # Propositional clauses after purity: 0
% 0.22/0.55 # Propositional unsat core size : 0
% 0.22/0.55 # Propositional preprocessing time : 0.000
% 0.22/0.55 # Propositional encoding time : 0.000
% 0.22/0.55 # Propositional solver time : 0.000
% 0.22/0.55 # Success case prop preproc time : 0.000
% 0.22/0.55 # Success case prop encoding time : 0.000
% 0.22/0.55 # Success case prop solver time : 0.000
% 0.22/0.55 # Current number of processed clauses : 44
% 0.22/0.55 # Positive orientable unit clauses : 11
% 0.22/0.55 # Positive unorientable unit clauses: 3
% 0.22/0.55 # Negative unit clauses : 1
% 0.22/0.55 # Non-unit-clauses : 29
% 0.22/0.55 # Current number of unprocessed clauses: 467
% 0.22/0.55 # ...number of literals in the above : 960
% 0.22/0.55 # Current number of archived formulas : 0
% 0.22/0.55 # Current number of archived clauses : 55
% 0.22/0.55 # Clause-clause subsumption calls (NU) : 550
% 0.22/0.55 # Rec. Clause-clause subsumption calls : 440
% 0.22/0.55 # Non-unit clause-clause subsumptions : 88
% 0.22/0.55 # Unit Clause-clause subsumption calls : 5
% 0.22/0.55 # Rewrite failures with RHS unbound : 0
% 0.22/0.55 # BW rewrite match attempts : 9
% 0.22/0.55 # BW rewrite match successes : 9
% 0.22/0.55 # Condensation attempts : 198
% 0.22/0.55 # Condensation successes : 1
% 0.22/0.55 # Termbank termtop insertions : 19649
% 0.22/0.55 # Search garbage collected termcells : 2242
% 0.22/0.55
% 0.22/0.55 # -------------------------------------------------
% 0.22/0.55 # User time : 0.026 s
% 0.22/0.55 # System time : 0.006 s
% 0.22/0.55 # Total time : 0.032 s
% 0.22/0.55 # Maximum resident set size: 2420 pages
% 0.22/0.55
% 0.22/0.55 # -------------------------------------------------
% 0.22/0.55 # User time : 0.033 s
% 0.22/0.55 # System time : 0.010 s
% 0.22/0.55 # Total time : 0.043 s
% 0.22/0.55 # Maximum resident set size: 2076 pages
% 0.22/0.55 % E---3.1 exiting
% 0.22/0.55 % E exiting
%------------------------------------------------------------------------------