TSTP Solution File: SEU182+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SEU182+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Thu Dec 30 01:32:38 EST 2010
% Result : Theorem 91.36s
% Output : Solution 91.80s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP24869/SEU182+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% not found
% Adding ~C to TBU ... ~t44_relat_1:
% ---- Iteration 1 (0 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... dt_k5_relat_1:
% CSA axiom dt_k5_relat_1 found
% Looking for CSA axiom ... reflexivity_r1_tarski:
% CSA axiom reflexivity_r1_tarski found
% Looking for CSA axiom ... rc1_relat_1:
% CSA axiom rc1_relat_1 found
% ---- Iteration 2 (3 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... d3_tarski:
% CSA axiom d3_tarski found
% Looking for CSA axiom ... antisymmetry_r2_hidden:
% CSA axiom antisymmetry_r2_hidden found
% Looking for CSA axiom ... rc1_xboole_0:
% rc2_xboole_0: CSA axiom rc2_xboole_0 found
% ---- Iteration 3 (6 axioms selected)
% Looking for TBU SAT ...
% yes
% Looking for TBU model ...
% not found
% Looking for CSA axiom ... rc1_xboole_0:
% d4_relat_1:
% CSA axiom d4_relat_1 found
% Looking for CSA axiom ... d8_relat_1:
% CSA axiom d8_relat_1 found
% Looking for CSA axiom ... rc1_subset_1:
% CSA axiom rc1_subset_1 found
% ---- Iteration 4 (9 axioms selected)
% Looking for TBU SAT ...
% no
% Looking for TBU UNS ...
% yes - theorem proved
% ---- Selection completed
% Selected axioms are ... :rc1_subset_1:d8_relat_1:d4_relat_1:rc2_xboole_0:antisymmetry_r2_hidden:d3_tarski:rc1_relat_1:reflexivity_r1_tarski:dt_k5_relat_1 (9)
% Unselected axioms are ... :rc1_xboole_0:rc2_subset_1:t3_subset:existence_m1_subset_1:fc1_zfmisc_1:t8_boole:t7_boole:t1_subset:commutativity_k2_tarski:d5_tarski:t4_subset:t2_subset:fc1_subset_1:fc1_xboole_0:fc2_subset_1:fc3_subset_1:t6_boole:t5_subset:dt_k1_relat_1:dt_k1_tarski:dt_k1_xboole_0:dt_k1_zfmisc_1:dt_k2_tarski:dt_k4_tarski:dt_m1_subset_1 (25)
% SZS status THM for /tmp/SystemOnTPTP24869/SEU182+1.tptp
% Looking for THM ...
% found
% SZS output start Solution for /tmp/SystemOnTPTP24869/SEU182+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=600 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 600s
% TreeLimitedRun: WC time limit is 1200s
% TreeLimitedRun: PID is 27041
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% # Preprocessing time : 0.012 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(2, axiom,![X1]:(relation(X1)=>![X2]:(relation(X2)=>![X3]:(relation(X3)=>(X3=relation_composition(X1,X2)<=>![X4]:![X5]:(in(ordered_pair(X4,X5),X3)<=>?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2))))))),file('/tmp/SRASS.s.p', d8_relat_1)).
% fof(3, axiom,![X1]:(relation(X1)=>![X2]:(X2=relation_dom(X1)<=>![X3]:(in(X3,X2)<=>?[X4]:in(ordered_pair(X3,X4),X1)))),file('/tmp/SRASS.s.p', d4_relat_1)).
% fof(6, axiom,![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2))),file('/tmp/SRASS.s.p', d3_tarski)).
% fof(9, axiom,![X1]:![X2]:((relation(X1)&relation(X2))=>relation(relation_composition(X1,X2))),file('/tmp/SRASS.s.p', dt_k5_relat_1)).
% fof(10, conjecture,![X1]:(relation(X1)=>![X2]:(relation(X2)=>subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)))),file('/tmp/SRASS.s.p', t44_relat_1)).
% fof(11, negated_conjecture,~(![X1]:(relation(X1)=>![X2]:(relation(X2)=>subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))))),inference(assume_negation,[status(cth)],[10])).
% fof(21, plain,![X1]:(~(relation(X1))|![X2]:(~(relation(X2))|![X3]:(~(relation(X3))|((~(X3=relation_composition(X1,X2))|![X4]:![X5]:((~(in(ordered_pair(X4,X5),X3))|?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2)))&(![X6]:(~(in(ordered_pair(X4,X6),X1))|~(in(ordered_pair(X6,X5),X2)))|in(ordered_pair(X4,X5),X3))))&(?[X4]:?[X5]:((~(in(ordered_pair(X4,X5),X3))|![X6]:(~(in(ordered_pair(X4,X6),X1))|~(in(ordered_pair(X6,X5),X2))))&(in(ordered_pair(X4,X5),X3)|?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2))))|X3=relation_composition(X1,X2)))))),inference(fof_nnf,[status(thm)],[2])).
% fof(22, plain,![X7]:(~(relation(X7))|![X8]:(~(relation(X8))|![X9]:(~(relation(X9))|((~(X9=relation_composition(X7,X8))|![X10]:![X11]:((~(in(ordered_pair(X10,X11),X9))|?[X12]:(in(ordered_pair(X10,X12),X7)&in(ordered_pair(X12,X11),X8)))&(![X13]:(~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))))&(?[X14]:?[X15]:((~(in(ordered_pair(X14,X15),X9))|![X16]:(~(in(ordered_pair(X14,X16),X7))|~(in(ordered_pair(X16,X15),X8))))&(in(ordered_pair(X14,X15),X9)|?[X17]:(in(ordered_pair(X14,X17),X7)&in(ordered_pair(X17,X15),X8))))|X9=relation_composition(X7,X8)))))),inference(variable_rename,[status(thm)],[21])).
% fof(23, plain,![X7]:(~(relation(X7))|![X8]:(~(relation(X8))|![X9]:(~(relation(X9))|((~(X9=relation_composition(X7,X8))|![X10]:![X11]:((~(in(ordered_pair(X10,X11),X9))|(in(ordered_pair(X10,esk2_5(X7,X8,X9,X10,X11)),X7)&in(ordered_pair(esk2_5(X7,X8,X9,X10,X11),X11),X8)))&(![X13]:(~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))))&(((~(in(ordered_pair(esk3_3(X7,X8,X9),esk4_3(X7,X8,X9)),X9))|![X16]:(~(in(ordered_pair(esk3_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk4_3(X7,X8,X9)),X8))))&(in(ordered_pair(esk3_3(X7,X8,X9),esk4_3(X7,X8,X9)),X9)|(in(ordered_pair(esk3_3(X7,X8,X9),esk5_3(X7,X8,X9)),X7)&in(ordered_pair(esk5_3(X7,X8,X9),esk4_3(X7,X8,X9)),X8))))|X9=relation_composition(X7,X8)))))),inference(skolemize,[status(esa)],[22])).
% fof(24, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X13]:![X16]:((((((((~(in(ordered_pair(esk3_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk4_3(X7,X8,X9)),X8)))|~(in(ordered_pair(esk3_3(X7,X8,X9),esk4_3(X7,X8,X9)),X9)))&(in(ordered_pair(esk3_3(X7,X8,X9),esk4_3(X7,X8,X9)),X9)|(in(ordered_pair(esk3_3(X7,X8,X9),esk5_3(X7,X8,X9)),X7)&in(ordered_pair(esk5_3(X7,X8,X9),esk4_3(X7,X8,X9)),X8))))|X9=relation_composition(X7,X8))&((((~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))&(~(in(ordered_pair(X10,X11),X9))|(in(ordered_pair(X10,esk2_5(X7,X8,X9,X10,X11)),X7)&in(ordered_pair(esk2_5(X7,X8,X9,X10,X11),X11),X8))))|~(X9=relation_composition(X7,X8))))|~(relation(X9)))|~(relation(X8)))|~(relation(X7))),inference(shift_quantors,[status(thm)],[23])).
% fof(25, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X13]:![X16]:((((((((~(in(ordered_pair(esk3_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk4_3(X7,X8,X9)),X8)))|~(in(ordered_pair(esk3_3(X7,X8,X9),esk4_3(X7,X8,X9)),X9)))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&((((((in(ordered_pair(esk3_3(X7,X8,X9),esk5_3(X7,X8,X9)),X7)|in(ordered_pair(esk3_3(X7,X8,X9),esk4_3(X7,X8,X9)),X9))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&(((((in(ordered_pair(esk5_3(X7,X8,X9),esk4_3(X7,X8,X9)),X8)|in(ordered_pair(esk3_3(X7,X8,X9),esk4_3(X7,X8,X9)),X9))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))))&(((((((~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&((((((in(ordered_pair(X10,esk2_5(X7,X8,X9,X10,X11)),X7)|~(in(ordered_pair(X10,X11),X9)))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&(((((in(ordered_pair(esk2_5(X7,X8,X9,X10,X11),X11),X8)|~(in(ordered_pair(X10,X11),X9)))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))))),inference(distribute,[status(thm)],[24])).
% cnf(27,plain,(in(ordered_pair(X4,esk2_5(X1,X2,X3,X4,X5)),X1)|~relation(X1)|~relation(X2)|~relation(X3)|X3!=relation_composition(X1,X2)|~in(ordered_pair(X4,X5),X3)),inference(split_conjunct,[status(thm)],[25])).
% fof(32, plain,![X1]:(~(relation(X1))|![X2]:((~(X2=relation_dom(X1))|![X3]:((~(in(X3,X2))|?[X4]:in(ordered_pair(X3,X4),X1))&(![X4]:~(in(ordered_pair(X3,X4),X1))|in(X3,X2))))&(?[X3]:((~(in(X3,X2))|![X4]:~(in(ordered_pair(X3,X4),X1)))&(in(X3,X2)|?[X4]:in(ordered_pair(X3,X4),X1)))|X2=relation_dom(X1)))),inference(fof_nnf,[status(thm)],[3])).
% fof(33, plain,![X5]:(~(relation(X5))|![X6]:((~(X6=relation_dom(X5))|![X7]:((~(in(X7,X6))|?[X8]:in(ordered_pair(X7,X8),X5))&(![X9]:~(in(ordered_pair(X7,X9),X5))|in(X7,X6))))&(?[X10]:((~(in(X10,X6))|![X11]:~(in(ordered_pair(X10,X11),X5)))&(in(X10,X6)|?[X12]:in(ordered_pair(X10,X12),X5)))|X6=relation_dom(X5)))),inference(variable_rename,[status(thm)],[32])).
% fof(34, plain,![X5]:(~(relation(X5))|![X6]:((~(X6=relation_dom(X5))|![X7]:((~(in(X7,X6))|in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5))&(![X9]:~(in(ordered_pair(X7,X9),X5))|in(X7,X6))))&(((~(in(esk7_2(X5,X6),X6))|![X11]:~(in(ordered_pair(esk7_2(X5,X6),X11),X5)))&(in(esk7_2(X5,X6),X6)|in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5)))|X6=relation_dom(X5)))),inference(skolemize,[status(esa)],[33])).
% fof(35, plain,![X5]:![X6]:![X7]:![X9]:![X11]:(((((~(in(ordered_pair(esk7_2(X5,X6),X11),X5))|~(in(esk7_2(X5,X6),X6)))&(in(esk7_2(X5,X6),X6)|in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5)))|X6=relation_dom(X5))&(((~(in(ordered_pair(X7,X9),X5))|in(X7,X6))&(~(in(X7,X6))|in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5)))|~(X6=relation_dom(X5))))|~(relation(X5))),inference(shift_quantors,[status(thm)],[34])).
% fof(36, plain,![X5]:![X6]:![X7]:![X9]:![X11]:(((((~(in(ordered_pair(esk7_2(X5,X6),X11),X5))|~(in(esk7_2(X5,X6),X6)))|X6=relation_dom(X5))|~(relation(X5)))&(((in(esk7_2(X5,X6),X6)|in(ordered_pair(esk7_2(X5,X6),esk8_2(X5,X6)),X5))|X6=relation_dom(X5))|~(relation(X5))))&((((~(in(ordered_pair(X7,X9),X5))|in(X7,X6))|~(X6=relation_dom(X5)))|~(relation(X5)))&(((~(in(X7,X6))|in(ordered_pair(X7,esk6_3(X5,X6,X7)),X5))|~(X6=relation_dom(X5)))|~(relation(X5))))),inference(distribute,[status(thm)],[35])).
% cnf(37,plain,(in(ordered_pair(X3,esk6_3(X1,X2,X3)),X1)|~relation(X1)|X2!=relation_dom(X1)|~in(X3,X2)),inference(split_conjunct,[status(thm)],[36])).
% cnf(38,plain,(in(X3,X2)|~relation(X1)|X2!=relation_dom(X1)|~in(ordered_pair(X3,X4),X1)),inference(split_conjunct,[status(thm)],[36])).
% fof(47, plain,![X1]:![X2]:((~(subset(X1,X2))|![X3]:(~(in(X3,X1))|in(X3,X2)))&(?[X3]:(in(X3,X1)&~(in(X3,X2)))|subset(X1,X2))),inference(fof_nnf,[status(thm)],[6])).
% fof(48, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&(?[X7]:(in(X7,X4)&~(in(X7,X5)))|subset(X4,X5))),inference(variable_rename,[status(thm)],[47])).
% fof(49, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&((in(esk10_2(X4,X5),X4)&~(in(esk10_2(X4,X5),X5)))|subset(X4,X5))),inference(skolemize,[status(esa)],[48])).
% fof(50, plain,![X4]:![X5]:![X6]:(((~(in(X6,X4))|in(X6,X5))|~(subset(X4,X5)))&((in(esk10_2(X4,X5),X4)&~(in(esk10_2(X4,X5),X5)))|subset(X4,X5))),inference(shift_quantors,[status(thm)],[49])).
% fof(51, plain,![X4]:![X5]:![X6]:(((~(in(X6,X4))|in(X6,X5))|~(subset(X4,X5)))&((in(esk10_2(X4,X5),X4)|subset(X4,X5))&(~(in(esk10_2(X4,X5),X5))|subset(X4,X5)))),inference(distribute,[status(thm)],[50])).
% cnf(52,plain,(subset(X1,X2)|~in(esk10_2(X1,X2),X2)),inference(split_conjunct,[status(thm)],[51])).
% cnf(53,plain,(subset(X1,X2)|in(esk10_2(X1,X2),X1)),inference(split_conjunct,[status(thm)],[51])).
% fof(61, plain,![X1]:![X2]:((~(relation(X1))|~(relation(X2)))|relation(relation_composition(X1,X2))),inference(fof_nnf,[status(thm)],[9])).
% fof(62, plain,![X3]:![X4]:((~(relation(X3))|~(relation(X4)))|relation(relation_composition(X3,X4))),inference(variable_rename,[status(thm)],[61])).
% cnf(63,plain,(relation(relation_composition(X1,X2))|~relation(X2)|~relation(X1)),inference(split_conjunct,[status(thm)],[62])).
% fof(64, negated_conjecture,?[X1]:(relation(X1)&?[X2]:(relation(X2)&~(subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))))),inference(fof_nnf,[status(thm)],[11])).
% fof(65, negated_conjecture,?[X3]:(relation(X3)&?[X4]:(relation(X4)&~(subset(relation_dom(relation_composition(X3,X4)),relation_dom(X3))))),inference(variable_rename,[status(thm)],[64])).
% fof(66, negated_conjecture,(relation(esk12_0)&(relation(esk13_0)&~(subset(relation_dom(relation_composition(esk12_0,esk13_0)),relation_dom(esk12_0))))),inference(skolemize,[status(esa)],[65])).
% cnf(67,negated_conjecture,(~subset(relation_dom(relation_composition(esk12_0,esk13_0)),relation_dom(esk12_0))),inference(split_conjunct,[status(thm)],[66])).
% cnf(68,negated_conjecture,(relation(esk13_0)),inference(split_conjunct,[status(thm)],[66])).
% cnf(69,negated_conjecture,(relation(esk12_0)),inference(split_conjunct,[status(thm)],[66])).
% cnf(82,plain,(in(X1,X2)|relation_dom(X3)!=X2|~relation(X3)|relation_composition(X3,X4)!=X5|~in(ordered_pair(X1,X6),X5)|~relation(X5)|~relation(X4)),inference(spm,[status(thm)],[38,27,theory(equality)])).
% cnf(128,plain,(in(X1,X2)|relation_composition(X3,X4)!=X5|relation_dom(X3)!=X2|~relation(X3)|~relation(X5)|~relation(X4)|relation_dom(X5)!=X6|~in(X1,X6)),inference(spm,[status(thm)],[82,37,theory(equality)])).
% cnf(149,plain,(in(X1,X2)|relation_dom(X3)!=X2|relation_dom(relation_composition(X3,X4))!=X5|~in(X1,X5)|~relation(X3)|~relation(relation_composition(X3,X4))|~relation(X4)),inference(er,[status(thm)],[128,theory(equality)])).
% cnf(150,plain,(in(X1,X2)|relation_dom(relation_composition(X3,X4))!=X5|relation_dom(X3)!=X2|~in(X1,X5)|~relation(X4)|~relation(X3)),inference(csr,[status(thm)],[149,63])).
% cnf(151,plain,(in(X1,X2)|relation_dom(X3)!=X2|~in(X1,relation_dom(relation_composition(X3,X4)))|~relation(X3)|~relation(X4)),inference(er,[status(thm)],[150,theory(equality)])).
% cnf(152,plain,(in(esk10_2(relation_dom(relation_composition(X1,X2)),X3),X4)|subset(relation_dom(relation_composition(X1,X2)),X3)|relation_dom(X1)!=X4|~relation(X1)|~relation(X2)),inference(spm,[status(thm)],[151,53,theory(equality)])).
% cnf(172,plain,(subset(relation_dom(relation_composition(X1,X2)),X3)|relation_dom(X1)!=X3|~relation(X1)|~relation(X2)),inference(spm,[status(thm)],[52,152,theory(equality)])).
% cnf(185,negated_conjecture,(~relation(esk12_0)|~relation(esk13_0)),inference(spm,[status(thm)],[67,172,theory(equality)])).
% cnf(186,negated_conjecture,($false|~relation(esk13_0)),inference(rw,[status(thm)],[185,69,theory(equality)])).
% cnf(187,negated_conjecture,($false|$false),inference(rw,[status(thm)],[186,68,theory(equality)])).
% cnf(188,negated_conjecture,($false),inference(cn,[status(thm)],[187,theory(equality)])).
% cnf(189,negated_conjecture,($false),188,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 86
% # ...of these trivial : 4
% # ...subsumed : 2
% # ...remaining for further processing: 80
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 0
% # Backward-rewritten : 0
% # Generated clauses : 108
% # ...of the previous two non-trivial : 97
% # Contextual simplify-reflections : 1
% # Paramodulations : 99
% # Factorizations : 6
% # Equation resolutions : 3
% # Current number of processed clauses: 56
% # Positive orientable unit clauses: 5
% # Positive unorientable unit clauses: 0
% # Negative unit clauses : 2
% # Non-unit-clauses : 49
% # Current number of unprocessed clauses: 59
% # ...number of literals in the above : 467
% # Clause-clause subsumption calls (NU) : 260
% # Rec. Clause-clause subsumption calls : 127
% # Unit Clause-clause subsumption calls : 0
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 0
% # Indexed BW rewrite successes : 0
% # Backwards rewriting index: 98 leaves, 1.47+/-1.303 terms/leaf
% # Paramod-from index: 22 leaves, 1.00+/-0.000 terms/leaf
% # Paramod-into index: 82 leaves, 1.21+/-0.487 terms/leaf
% # -------------------------------------------------
% # User time : 0.021 s
% # System time : 0.004 s
% # Total time : 0.025 s
% # Maximum resident set size: 0 pages
% PrfWatch: 0.10 CPU 0.19 WC
% FINAL PrfWatch: 0.10 CPU 0.19 WC
% SZS output end Solution for /tmp/SystemOnTPTP24869/SEU182+1.tptp
%
%------------------------------------------------------------------------------