TSTP Solution File: SEU166+3 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SEU166+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:30:42 EDT 2023
% Result : Theorem 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 133 ( 31 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 156 ( 66 ~; 70 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-4 aty)
% Number of variables : 126 ( 0 sgn; 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.d5xi5133Aa/E---3.1_27410.p',d2_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/tmp/tmp.d5xi5133Aa/E---3.1_27410.p',d5_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.d5xi5133Aa/E---3.1_27410.p',commutativity_k2_tarski) ).
fof(t118_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.d5xi5133Aa/E---3.1_27410.p',t118_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.d5xi5133Aa/E---3.1_27410.p',d3_tarski) ).
fof(c_0_5,plain,
! [X11,X12,X13,X14,X17,X18,X19,X20,X21,X22,X24,X25] :
( ( in(esk1_4(X11,X12,X13,X14),X11)
| ~ in(X14,X13)
| X13 != cartesian_product2(X11,X12) )
& ( in(esk2_4(X11,X12,X13,X14),X12)
| ~ in(X14,X13)
| X13 != cartesian_product2(X11,X12) )
& ( X14 = ordered_pair(esk1_4(X11,X12,X13,X14),esk2_4(X11,X12,X13,X14))
| ~ in(X14,X13)
| X13 != cartesian_product2(X11,X12) )
& ( ~ in(X18,X11)
| ~ in(X19,X12)
| X17 != ordered_pair(X18,X19)
| in(X17,X13)
| X13 != cartesian_product2(X11,X12) )
& ( ~ in(esk3_3(X20,X21,X22),X22)
| ~ in(X24,X20)
| ~ in(X25,X21)
| esk3_3(X20,X21,X22) != ordered_pair(X24,X25)
| X22 = cartesian_product2(X20,X21) )
& ( in(esk4_3(X20,X21,X22),X20)
| in(esk3_3(X20,X21,X22),X22)
| X22 = cartesian_product2(X20,X21) )
& ( in(esk5_3(X20,X21,X22),X21)
| in(esk3_3(X20,X21,X22),X22)
| X22 = cartesian_product2(X20,X21) )
& ( esk3_3(X20,X21,X22) = ordered_pair(esk4_3(X20,X21,X22),esk5_3(X20,X21,X22))
| in(esk3_3(X20,X21,X22),X22)
| X22 = cartesian_product2(X20,X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_zfmisc_1])])])])])]) ).
fof(c_0_6,plain,
! [X34,X35] : ordered_pair(X34,X35) = unordered_pair(unordered_pair(X34,X35),singleton(X34)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_7,plain,
( in(X5,X6)
| ~ in(X1,X2)
| ~ in(X3,X4)
| X5 != ordered_pair(X1,X3)
| X6 != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( in(X5,X6)
| X6 != cartesian_product2(X2,X4)
| X5 != unordered_pair(unordered_pair(X1,X3),singleton(X1))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_10,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_11,plain,
( X1 = ordered_pair(esk1_4(X2,X3,X4,X1),esk2_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( X1 = unordered_pair(unordered_pair(esk1_4(X2,X3,X4,X1),esk2_4(X2,X3,X4,X1)),singleton(esk1_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[c_0_11,c_0_8]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
inference(assume_negation,[status(cth)],[t118_zfmisc_1]) ).
cnf(c_0_16,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( unordered_pair(singleton(esk1_4(X1,X2,cartesian_product2(X1,X2),X3)),unordered_pair(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),esk2_4(X1,X2,cartesian_product2(X1,X2),X3))) = X3
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_13])]) ).
cnf(c_0_18,plain,
( in(esk2_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_19,plain,
! [X28,X29,X30,X31,X32] :
( ( ~ subset(X28,X29)
| ~ in(X30,X28)
| in(X30,X29) )
& ( in(esk6_2(X31,X32),X31)
| subset(X31,X32) )
& ( ~ in(esk6_2(X31,X32),X32)
| subset(X31,X32) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
fof(c_0_20,negated_conjecture,
( subset(esk9_0,esk10_0)
& ( ~ subset(cartesian_product2(esk9_0,esk11_0),cartesian_product2(esk10_0,esk11_0))
| ~ subset(cartesian_product2(esk11_0,esk9_0),cartesian_product2(esk11_0,esk10_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_21,plain,
( in(X1,cartesian_product2(X2,X3))
| ~ in(esk2_4(X4,X5,cartesian_product2(X4,X5),X1),X3)
| ~ in(esk1_4(X4,X5,cartesian_product2(X4,X5),X1),X2)
| ~ in(X1,cartesian_product2(X4,X5)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
subset(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( in(X1,cartesian_product2(X2,X3))
| ~ in(esk1_4(X4,X3,cartesian_product2(X4,X3),X1),X2)
| ~ in(X1,cartesian_product2(X4,X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( in(X1,esk10_0)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( in(esk1_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,cartesian_product2(esk10_0,X2))
| ~ in(esk1_4(X3,X2,cartesian_product2(X3,X2),X1),esk9_0)
| ~ in(X1,cartesian_product2(X3,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( in(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,cartesian_product2(X2,esk10_0))
| ~ in(esk2_4(X3,X4,cartesian_product2(X3,X4),X1),esk9_0)
| ~ in(esk1_4(X3,X4,cartesian_product2(X3,X4),X1),X2)
| ~ in(X1,cartesian_product2(X3,X4)) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_31,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( in(X1,cartesian_product2(esk10_0,X2))
| ~ in(X1,cartesian_product2(esk9_0,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( in(X1,cartesian_product2(X2,esk10_0))
| ~ in(esk1_4(X3,esk9_0,cartesian_product2(X3,esk9_0),X1),X2)
| ~ in(X1,cartesian_product2(X3,esk9_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
( subset(X1,cartesian_product2(esk10_0,X2))
| ~ in(esk6_2(X1,cartesian_product2(esk10_0,X2)),cartesian_product2(esk9_0,X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( in(esk6_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_36,negated_conjecture,
( in(X1,cartesian_product2(X2,esk10_0))
| ~ in(X1,cartesian_product2(X2,esk9_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( ~ subset(cartesian_product2(esk9_0,esk11_0),cartesian_product2(esk10_0,esk11_0))
| ~ subset(cartesian_product2(esk11_0,esk9_0),cartesian_product2(esk11_0,esk10_0)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_38,negated_conjecture,
subset(cartesian_product2(esk9_0,X1),cartesian_product2(esk10_0,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( subset(X1,cartesian_product2(X2,esk10_0))
| ~ in(esk6_2(X1,cartesian_product2(X2,esk10_0)),cartesian_product2(X2,esk9_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
~ subset(cartesian_product2(esk11_0,esk9_0),cartesian_product2(esk11_0,esk10_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
subset(cartesian_product2(X1,esk9_0),cartesian_product2(X1,esk10_0)),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU166+3 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 2400
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Oct 2 08:53:05 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.46 Running first-order model finding
% 0.20/0.46 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.d5xi5133Aa/E---3.1_27410.p
% 0.20/0.48 # Version: 3.1pre001
% 0.20/0.48 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.48 # Starting new_bool_3 with 300s (1) cores
% 0.20/0.48 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.48 # Starting sh5l with 300s (1) cores
% 0.20/0.48 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 27497 completed with status 0
% 0.20/0.48 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.20/0.48 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.48 # No SInE strategy applied
% 0.20/0.48 # Search class: FGHSS-FFMF32-MFFFFFNN
% 0.20/0.48 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.48 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 811s (1) cores
% 0.20/0.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.20/0.48 # Starting new_bool_3 with 136s (1) cores
% 0.20/0.48 # Starting new_bool_1 with 136s (1) cores
% 0.20/0.48 # Starting sh5l with 136s (1) cores
% 0.20/0.48 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 27508 completed with status 0
% 0.20/0.48 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.20/0.48 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.48 # No SInE strategy applied
% 0.20/0.48 # Search class: FGHSS-FFMF32-MFFFFFNN
% 0.20/0.48 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.48 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 811s (1) cores
% 0.20/0.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.20/0.48 # Preprocessing time : 0.001 s
% 0.20/0.48 # Presaturation interreduction done
% 0.20/0.48
% 0.20/0.48 # Proof found!
% 0.20/0.48 # SZS status Theorem
% 0.20/0.48 # SZS output start CNFRefutation
% See solution above
% 0.20/0.48 # Parsed axioms : 10
% 0.20/0.48 # Removed by relevancy pruning/SinE : 0
% 0.20/0.48 # Initial clauses : 20
% 0.20/0.48 # Removed in clause preprocessing : 1
% 0.20/0.48 # Initial clauses in saturation : 19
% 0.20/0.48 # Processed clauses : 241
% 0.20/0.48 # ...of these trivial : 0
% 0.20/0.48 # ...subsumed : 88
% 0.20/0.48 # ...remaining for further processing : 153
% 0.20/0.48 # Other redundant clauses eliminated : 5
% 0.20/0.48 # Clauses deleted for lack of memory : 0
% 0.20/0.48 # Backward-subsumed : 0
% 0.20/0.48 # Backward-rewritten : 2
% 0.20/0.48 # Generated clauses : 303
% 0.20/0.48 # ...of the previous two non-redundant : 299
% 0.20/0.48 # ...aggressively subsumed : 0
% 0.20/0.48 # Contextual simplify-reflections : 0
% 0.20/0.48 # Paramodulations : 299
% 0.20/0.48 # Factorizations : 0
% 0.20/0.48 # NegExts : 0
% 0.20/0.48 # Equation resolutions : 5
% 0.20/0.48 # Total rewrite steps : 11
% 0.20/0.48 # Propositional unsat checks : 0
% 0.20/0.48 # Propositional check models : 0
% 0.20/0.48 # Propositional check unsatisfiable : 0
% 0.20/0.48 # Propositional clauses : 0
% 0.20/0.48 # Propositional clauses after purity: 0
% 0.20/0.48 # Propositional unsat core size : 0
% 0.20/0.48 # Propositional preprocessing time : 0.000
% 0.20/0.48 # Propositional encoding time : 0.000
% 0.20/0.48 # Propositional solver time : 0.000
% 0.20/0.48 # Success case prop preproc time : 0.000
% 0.20/0.48 # Success case prop encoding time : 0.000
% 0.20/0.48 # Success case prop solver time : 0.000
% 0.20/0.48 # Current number of processed clauses : 128
% 0.20/0.48 # Positive orientable unit clauses : 8
% 0.20/0.48 # Positive unorientable unit clauses: 1
% 0.20/0.48 # Negative unit clauses : 7
% 0.20/0.48 # Non-unit-clauses : 112
% 0.20/0.48 # Current number of unprocessed clauses: 96
% 0.20/0.48 # ...number of literals in the above : 360
% 0.20/0.48 # Current number of archived formulas : 0
% 0.20/0.48 # Current number of archived clauses : 22
% 0.20/0.48 # Clause-clause subsumption calls (NU) : 3863
% 0.20/0.48 # Rec. Clause-clause subsumption calls : 2982
% 0.20/0.48 # Non-unit clause-clause subsumptions : 71
% 0.20/0.48 # Unit Clause-clause subsumption calls : 73
% 0.20/0.48 # Rewrite failures with RHS unbound : 0
% 0.20/0.48 # BW rewrite match attempts : 10
% 0.20/0.48 # BW rewrite match successes : 2
% 0.20/0.48 # Condensation attempts : 0
% 0.20/0.48 # Condensation successes : 0
% 0.20/0.48 # Termbank termtop insertions : 7731
% 0.20/0.48
% 0.20/0.48 # -------------------------------------------------
% 0.20/0.48 # User time : 0.011 s
% 0.20/0.48 # System time : 0.005 s
% 0.20/0.48 # Total time : 0.016 s
% 0.20/0.48 # Maximum resident set size: 1788 pages
% 0.20/0.48
% 0.20/0.48 # -------------------------------------------------
% 0.20/0.48 # User time : 0.052 s
% 0.20/0.48 # System time : 0.009 s
% 0.20/0.48 # Total time : 0.062 s
% 0.20/0.48 # Maximum resident set size: 1688 pages
% 0.20/0.48 % E---3.1 exiting
%------------------------------------------------------------------------------