TSTP Solution File: NUN057+2 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : NUN057+2 : TPTP v8.2.0. Released v7.3.0.
% 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 : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:15:49 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 24 unt; 0 def)
% Number of atoms : 188 ( 47 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 232 ( 99 ~; 82 |; 51 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 151 ( 4 sgn 33 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( ? [X32] :
( r1(X32)
& r3(X30,X32,X31) )
& X31 = X30 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X17] :
( ? [X18] :
( r2(X15,X18)
& r3(X14,X18,X17) )
& X17 = X16 )
& ? [X19] :
( r2(X19,X16)
& r3(X14,X15,X19) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(twoplustwoeqfour,conjecture,
? [X39] :
( ? [X22] :
( X39 = X22
& ? [X23] :
( r2(X23,X22)
& ? [X16] :
( r2(X16,X23)
& ? [X25] :
( r2(X25,X16)
& ? [X34] :
( r1(X34)
& r2(X34,X25) ) ) ) ) )
& ? [X17] :
( r3(X17,X17,X39)
& ? [X19] :
( r2(X19,X17)
& ? [X31] :
( r1(X31)
& r2(X31,X19) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',twoplustwoeqfour) ).
fof(c_0_6,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_7,plain,
! [X75] :
( r1(esk11_1(X75))
& r3(X75,esk11_1(X75),esk10_1(X75))
& esk10_1(X75) = X75 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_8,plain,
! [X74] :
( ( r1(X74)
| ~ r1(X74) )
& ( X74 = esk9_0
| ~ r1(X74) )
& ( r1(X74)
| X74 != esk9_0 )
& ( X74 = esk9_0
| X74 != esk9_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
cnf(c_0_10,plain,
r3(X1,esk11_1(X1),esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
esk10_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( X1 = esk9_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
r1(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_14,plain,
! [X78,X79,X81] :
( ( r3(X78,X79,X81)
| ~ r3(X78,X79,X81) )
& ( X81 = esk12_2(X78,X79)
| ~ r3(X78,X79,X81) )
& ( r3(X78,X79,X81)
| X81 != esk12_2(X78,X79) )
& ( X81 = esk12_2(X78,X79)
| X81 != esk12_2(X78,X79) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_15,plain,
r3(X1,esk11_1(X1),X1),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
esk11_1(X1) = esk9_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X56,X57] :
( r2(X57,esk4_2(X56,X57))
& r3(X56,esk4_2(X56,X57),esk3_2(X56,X57))
& esk3_2(X56,X57) = esk2_2(X56,X57)
& r2(esk5_2(X56,X57),esk2_2(X56,X57))
& r3(X56,X57,esk5_2(X56,X57)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_18,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
cnf(c_0_19,plain,
( X1 = esk12_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
r3(X1,esk9_0,X1),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
r3(X1,X2,esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,negated_conjecture,
~ ? [X39] :
( ? [X22] :
( X39 = X22
& ? [X23] :
( r2(X23,X22)
& ? [X16] :
( r2(X16,X23)
& ? [X25] :
( r2(X25,X16)
& ? [X34] :
( r1(X34)
& r2(X34,X25) ) ) ) ) )
& ? [X17] :
( r3(X17,X17,X39)
& ? [X19] :
( r2(X19,X17)
& ? [X31] :
( r1(X31)
& r2(X31,X19) ) ) ) ),
inference(assume_negation,[status(cth)],[twoplustwoeqfour]) ).
fof(c_0_23,plain,
! [X53,X55] :
( ( r2(X53,X55)
| ~ r2(X53,X55) )
& ( X55 = esk1_1(X53)
| ~ r2(X53,X55) )
& ( r2(X53,X55)
| X55 != esk1_1(X53) )
& ( X55 = esk1_1(X53)
| X55 != esk1_1(X53) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_24,plain,
r2(esk5_2(X1,X2),esk2_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
esk3_2(X1,X2) = esk2_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
esk12_2(X1,esk9_0) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
esk12_2(X1,X2) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
fof(c_0_28,negated_conjecture,
! [X44,X45,X46,X47,X48,X49,X50,X51,X52] :
( X44 != X45
| ~ r2(X46,X45)
| ~ r2(X47,X46)
| ~ r2(X48,X47)
| ~ r1(X49)
| ~ r2(X49,X48)
| ~ r3(X50,X50,X44)
| ~ r2(X51,X50)
| ~ r1(X52)
| ~ r2(X52,X51) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
cnf(c_0_29,plain,
( X1 = esk1_1(X2)
| ~ r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
r2(X1,esk4_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,plain,
r2(esk5_2(X1,X2),esk3_2(X1,X2)),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
esk5_2(X1,esk9_0) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( X1 != X2
| ~ r2(X3,X2)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5)
| ~ r3(X7,X7,X1)
| ~ r2(X8,X7)
| ~ r1(X9)
| ~ r2(X9,X8) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
r3(X1,esk4_2(X1,X2),esk3_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_35,plain,
esk4_2(X1,X2) = esk1_1(X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
r2(X1,esk3_2(X1,esk9_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( ~ r3(X1,X1,X2)
| ~ r2(X3,X4)
| ~ r2(X4,X1)
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r2(X7,X8)
| ~ r2(X8,X2)
| ~ r1(X3)
| ~ r1(X5) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
r3(X1,esk1_1(X2),esk3_2(X1,X2)),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
esk3_2(X1,esk9_0) = esk1_1(X1),
inference(spm,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( ~ r2(X1,esk3_2(esk1_1(X2),X2))
| ~ r2(X3,esk1_1(X2))
| ~ r2(X4,X3)
| ~ r2(X5,X6)
| ~ r2(X6,X7)
| ~ r2(X7,X1)
| ~ r1(X4)
| ~ r1(X5) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
( X1 = esk5_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_42,plain,
r3(X1,esk1_1(esk9_0),esk1_1(X1)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( ~ r2(X1,esk5_2(esk1_1(X2),X2))
| ~ r2(X3,esk1_1(X2))
| ~ r2(X4,X3)
| ~ r2(X5,X6)
| ~ r2(X6,X1)
| ~ r1(X4)
| ~ r1(X5) ),
inference(spm,[status(thm)],[c_0_40,c_0_31]) ).
cnf(c_0_44,plain,
esk5_2(X1,esk1_1(esk9_0)) = esk1_1(X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( r2(X1,X2)
| X2 != esk1_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_46,negated_conjecture,
( ~ r2(X1,esk1_1(esk1_1(esk1_1(esk9_0))))
| ~ r2(X2,esk1_1(esk1_1(esk9_0)))
| ~ r2(X3,X2)
| ~ r2(X4,X5)
| ~ r2(X5,X1)
| ~ r1(X3)
| ~ r1(X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
r2(X1,esk1_1(X1)),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( ~ r2(X1,esk1_1(esk1_1(esk9_0)))
| ~ r2(X2,esk1_1(esk1_1(esk9_0)))
| ~ r2(X3,X1)
| ~ r2(X4,X2)
| ~ r1(X3)
| ~ r1(X4) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,negated_conjecture,
( ~ r2(X1,esk1_1(esk1_1(esk9_0)))
| ~ r2(X2,esk1_1(esk9_0))
| ~ r2(X3,X1)
| ~ r1(X2)
| ~ r1(X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_50,plain,
( r1(X1)
| X1 != esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_51,negated_conjecture,
( ~ r2(X1,esk1_1(esk9_0))
| ~ r2(X2,esk1_1(esk9_0))
| ~ r1(X1)
| ~ r1(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_47]) ).
cnf(c_0_52,plain,
r1(esk9_0),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( ~ r2(X1,esk1_1(esk9_0))
| ~ r1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_47]),c_0_52])]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_47]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUN057+2 : TPTP v8.2.0. Released v7.3.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n010.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 14:54:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running first-order model finding
% 0.21/0.47 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 # Version: 3.1.0
% 0.21/0.49 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.49 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.49 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.49 # Starting sh5l with 300s (1) cores
% 0.21/0.49 # new_bool_3 with pid 11097 completed with status 0
% 0.21/0.49 # Result found by new_bool_3
% 0.21/0.49 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.49 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.49 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.49 # Search class: FGHSM-FFSF21-SFFFFFNN
% 0.21/0.49 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49 # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.49 # SAT001_MinMin_p005000_rr_RG with pid 11100 completed with status 0
% 0.21/0.49 # Result found by SAT001_MinMin_p005000_rr_RG
% 0.21/0.49 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.21/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.49 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.21/0.49 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.49 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.49 # Search class: FGHSM-FFSF21-SFFFFFNN
% 0.21/0.49 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.49 # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.49 # Preprocessing time : 0.001 s
% 0.21/0.49 # Presaturation interreduction done
% 0.21/0.49
% 0.21/0.49 # Proof found!
% 0.21/0.49 # SZS status Theorem
% 0.21/0.49 # SZS output start CNFRefutation
% See solution above
% 0.21/0.49 # Parsed axioms : 12
% 0.21/0.49 # Removed by relevancy pruning/SinE : 3
% 0.21/0.49 # Initial clauses : 27
% 0.21/0.49 # Removed in clause preprocessing : 6
% 0.21/0.49 # Initial clauses in saturation : 21
% 0.21/0.49 # Processed clauses : 112
% 0.21/0.49 # ...of these trivial : 0
% 0.21/0.49 # ...subsumed : 21
% 0.21/0.49 # ...remaining for further processing : 91
% 0.21/0.49 # Other redundant clauses eliminated : 6
% 0.21/0.49 # Clauses deleted for lack of memory : 0
% 0.21/0.49 # Backward-subsumed : 2
% 0.21/0.49 # Backward-rewritten : 9
% 0.21/0.49 # Generated clauses : 118
% 0.21/0.49 # ...of the previous two non-redundant : 114
% 0.21/0.49 # ...aggressively subsumed : 0
% 0.21/0.49 # Contextual simplify-reflections : 1
% 0.21/0.49 # Paramodulations : 112
% 0.21/0.49 # Factorizations : 0
% 0.21/0.49 # NegExts : 0
% 0.21/0.49 # Equation resolutions : 6
% 0.21/0.49 # Disequality decompositions : 0
% 0.21/0.49 # Total rewrite steps : 28
% 0.21/0.49 # ...of those cached : 10
% 0.21/0.49 # Propositional unsat checks : 0
% 0.21/0.49 # Propositional check models : 0
% 0.21/0.49 # Propositional check unsatisfiable : 0
% 0.21/0.49 # Propositional clauses : 0
% 0.21/0.49 # Propositional clauses after purity: 0
% 0.21/0.49 # Propositional unsat core size : 0
% 0.21/0.49 # Propositional preprocessing time : 0.000
% 0.21/0.49 # Propositional encoding time : 0.000
% 0.21/0.49 # Propositional solver time : 0.000
% 0.21/0.49 # Success case prop preproc time : 0.000
% 0.21/0.49 # Success case prop encoding time : 0.000
% 0.21/0.49 # Success case prop solver time : 0.000
% 0.21/0.49 # Current number of processed clauses : 53
% 0.21/0.49 # Positive orientable unit clauses : 15
% 0.21/0.49 # Positive unorientable unit clauses: 0
% 0.21/0.49 # Negative unit clauses : 2
% 0.21/0.49 # Non-unit-clauses : 36
% 0.21/0.49 # Current number of unprocessed clauses: 43
% 0.21/0.49 # ...number of literals in the above : 186
% 0.21/0.49 # Current number of archived formulas : 0
% 0.21/0.49 # Current number of archived clauses : 32
% 0.21/0.49 # Clause-clause subsumption calls (NU) : 984
% 0.21/0.49 # Rec. Clause-clause subsumption calls : 347
% 0.21/0.49 # Non-unit clause-clause subsumptions : 21
% 0.21/0.49 # Unit Clause-clause subsumption calls : 24
% 0.21/0.49 # Rewrite failures with RHS unbound : 0
% 0.21/0.49 # BW rewrite match attempts : 13
% 0.21/0.49 # BW rewrite match successes : 9
% 0.21/0.49 # Condensation attempts : 0
% 0.21/0.49 # Condensation successes : 0
% 0.21/0.49 # Termbank termtop insertions : 3156
% 0.21/0.49 # Search garbage collected termcells : 355
% 0.21/0.49
% 0.21/0.49 # -------------------------------------------------
% 0.21/0.49 # User time : 0.007 s
% 0.21/0.49 # System time : 0.005 s
% 0.21/0.49 # Total time : 0.012 s
% 0.21/0.49 # Maximum resident set size: 1852 pages
% 0.21/0.49
% 0.21/0.49 # -------------------------------------------------
% 0.21/0.49 # User time : 0.007 s
% 0.21/0.49 # System time : 0.008 s
% 0.21/0.49 # Total time : 0.015 s
% 0.21/0.49 # Maximum resident set size: 1744 pages
% 0.21/0.49 % E---3.1 exiting
%------------------------------------------------------------------------------