# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
# and selection function SelectComplexExceptUniqMaxHorn.
#
# Preprocessing time       : 0.019 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t51_surrealc, conjecture, ![X1]:(v2_surreal0(X1)=>![X2]:(v2_surreal0(X2)=>![X3]:(v2_surreal0(X3)=>((r1_surrealo(X1,X2)&r1_surrealo(X2,X3))=>r1_surrealo(k4_surrealc(X2),k8_surrealr(k4_surrealc(X1),k4_surrealc(X3))))))), file('surrealc/surrealc__t51_surrealc', t51_surrealc)).
fof(d6_surrealc, axiom, ![X1]:(v2_surreal0(X1)=>((r1_surrealo(k11_surreal0,X1)=>k4_surrealc(X1)=X1)&(~(r1_surrealo(k11_surreal0,X1))=>k4_surrealc(X1)=k2_surrealr(X1)))), file('surrealc/surrealc__t51_surrealc', d6_surrealc)).
fof(commutativity_k8_surrealr, axiom, ![X1, X2]:((v2_surreal0(X1)&v2_surreal0(X2))=>k8_surrealr(X1,X2)=k8_surrealr(X2,X1)), file('surrealc/surrealc__t51_surrealc', commutativity_k8_surrealr)).
fof(t43_surrealr, axiom, ![X1]:(v2_surreal0(X1)=>![X2]:(v2_surreal0(X2)=>![X3]:(v2_surreal0(X3)=>![X4]:(v2_surreal0(X4)=>((r1_surrealo(X1,X2)&r1_surrealo(X3,X4))=>r1_surrealo(k8_surrealr(X1,X3),k8_surrealr(X2,X4))))))), file('surrealc/surrealc__t51_surrealc', t43_surrealr)).
fof(rd3_surrealr, axiom, ![X1]:(v2_surreal0(X1)=>k8_surrealr(X1,k11_surreal0)=X1), file('surrealc/surrealc__t51_surrealc', rd3_surrealr)).
fof(t4_surrealo, axiom, ![X1]:(v2_surreal0(X1)=>![X2]:(v2_surreal0(X2)=>![X3]:(v2_surreal0(X3)=>((r5_surreal0(X1,X2)&r5_surreal0(X2,X3))=>r5_surreal0(X1,X3))))), file('surrealc/surrealc__t51_surrealc', t4_surrealo)).
fof(redefinition_r1_surrealo, axiom, ![X1, X2]:((v2_surreal0(X1)&v2_surreal0(X2))=>(r1_surrealo(X1,X2)<=>r5_surreal0(X1,X2))), file('surrealc/surrealc__t51_surrealc', redefinition_r1_surrealo)).
fof(dt_k11_surreal0, axiom, v2_surreal0(k11_surreal0), file('surrealc/surrealc__t51_surrealc', dt_k11_surreal0)).
fof(t10_surrealr, axiom, ![X1]:(v2_surreal0(X1)=>![X2]:(v2_surreal0(X2)=>(r1_surrealo(X1,X2)<=>r1_surrealo(k2_surrealr(X2),k2_surrealr(X1))))), file('surrealc/surrealc__t51_surrealc', t10_surrealr)).
fof(t31_surrealc, axiom, ![X1]:(v2_surreal0(X1)=>r1_surrealo(k11_surreal0,k4_surrealc(X1))), file('surrealc/surrealc__t51_surrealc', t31_surrealc)).
fof(dt_k4_surrealc, axiom, ![X1]:(v2_surreal0(X1)=>v2_surreal0(k4_surrealc(X1))), file('surrealc/surrealc__t51_surrealc', dt_k4_surrealc)).
fof(c_0_11, negated_conjecture, ~(![X1]:(v2_surreal0(X1)=>![X2]:(v2_surreal0(X2)=>![X3]:(v2_surreal0(X3)=>((r1_surrealo(X1,X2)&r1_surrealo(X2,X3))=>r1_surrealo(k4_surrealc(X2),k8_surrealr(k4_surrealc(X1),k4_surrealc(X3)))))))), inference(assume_negation,[status(cth)],[t51_surrealc])).
fof(c_0_12, plain, ![X1]:(v2_surreal0(X1)=>((r1_surrealo(k11_surreal0,X1)=>k4_surrealc(X1)=X1)&(~r1_surrealo(k11_surreal0,X1)=>k4_surrealc(X1)=k2_surrealr(X1)))), inference(fof_simplification,[status(thm)],[d6_surrealc])).
fof(c_0_13, negated_conjecture, (v2_surreal0(esk1_0)&(v2_surreal0(esk2_0)&(v2_surreal0(esk3_0)&((r1_surrealo(esk1_0,esk2_0)&r1_surrealo(esk2_0,esk3_0))&~r1_surrealo(k4_surrealc(esk2_0),k8_surrealr(k4_surrealc(esk1_0),k4_surrealc(esk3_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])).
fof(c_0_14, plain, ![X30]:((~r1_surrealo(k11_surreal0,X30)|k4_surrealc(X30)=X30|~v2_surreal0(X30))&(r1_surrealo(k11_surreal0,X30)|k4_surrealc(X30)=k2_surrealr(X30)|~v2_surreal0(X30))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])).
cnf(c_0_15, negated_conjecture, (~r1_surrealo(k4_surrealc(esk2_0),k8_surrealr(k4_surrealc(esk1_0),k4_surrealc(esk3_0)))), inference(split_conjunct,[status(thm)],[c_0_13])).
cnf(c_0_16, plain, (k4_surrealc(X1)=X1|~r1_surrealo(k11_surreal0,X1)|~v2_surreal0(X1)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_17, negated_conjecture, (v2_surreal0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_13])).
cnf(c_0_18, negated_conjecture, (~r1_surrealo(k4_surrealc(esk2_0),k8_surrealr(k4_surrealc(esk1_0),esk3_0))|~r1_surrealo(k11_surreal0,esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_17])])).
cnf(c_0_19, negated_conjecture, (v2_surreal0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_20, plain, ![X28, X29]:(~v2_surreal0(X28)|~v2_surreal0(X29)|k8_surrealr(X28,X29)=k8_surrealr(X29,X28)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k8_surrealr])])).
fof(c_0_21, plain, ![X38, X39, X40, X41]:(~v2_surreal0(X38)|(~v2_surreal0(X39)|(~v2_surreal0(X40)|(~v2_surreal0(X41)|(~r1_surrealo(X38,X39)|~r1_surrealo(X40,X41)|r1_surrealo(k8_surrealr(X38,X40),k8_surrealr(X39,X41))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_surrealr])])])).
fof(c_0_22, plain, ![X32]:(~v2_surreal0(X32)|k8_surrealr(X32,k11_surreal0)=X32), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rd3_surrealr])])).
fof(c_0_23, plain, ![X42, X43, X44]:(~v2_surreal0(X42)|(~v2_surreal0(X43)|(~v2_surreal0(X44)|(~r5_surreal0(X42,X43)|~r5_surreal0(X43,X44)|r5_surreal0(X42,X44))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_surrealo])])])).
fof(c_0_24, plain, ![X33, X34]:((~r1_surrealo(X33,X34)|r5_surreal0(X33,X34)|(~v2_surreal0(X33)|~v2_surreal0(X34)))&(~r5_surreal0(X33,X34)|r1_surrealo(X33,X34)|(~v2_surreal0(X33)|~v2_surreal0(X34)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_surrealo])])])).
cnf(c_0_25, negated_conjecture, (~r1_surrealo(esk2_0,k8_surrealr(k4_surrealc(esk1_0),esk3_0))|~r1_surrealo(k11_surreal0,esk3_0)|~r1_surrealo(k11_surreal0,esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_16]), c_0_19])])).
cnf(c_0_26, plain, (k8_surrealr(X1,X2)=k8_surrealr(X2,X1)|~v2_surreal0(X1)|~v2_surreal0(X2)), inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_27, plain, (r1_surrealo(k8_surrealr(X1,X3),k8_surrealr(X2,X4))|~v2_surreal0(X1)|~v2_surreal0(X2)|~v2_surreal0(X3)|~v2_surreal0(X4)|~r1_surrealo(X1,X2)|~r1_surrealo(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_21])).
cnf(c_0_28, plain, (k8_surrealr(X1,k11_surreal0)=X1|~v2_surreal0(X1)), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_29, plain, (v2_surreal0(k11_surreal0)), inference(split_conjunct,[status(thm)],[dt_k11_surreal0])).
cnf(c_0_30, plain, (r5_surreal0(X1,X3)|~v2_surreal0(X1)|~v2_surreal0(X2)|~v2_surreal0(X3)|~r5_surreal0(X1,X2)|~r5_surreal0(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_31, plain, (r5_surreal0(X1,X2)|~r1_surrealo(X1,X2)|~v2_surreal0(X1)|~v2_surreal0(X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
fof(c_0_32, plain, ![X35, X36]:((~r1_surrealo(X35,X36)|r1_surrealo(k2_surrealr(X36),k2_surrealr(X35))|~v2_surreal0(X36)|~v2_surreal0(X35))&(~r1_surrealo(k2_surrealr(X36),k2_surrealr(X35))|r1_surrealo(X35,X36)|~v2_surreal0(X36)|~v2_surreal0(X35))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_surrealr])])])])).
cnf(c_0_33, plain, (r1_surrealo(k11_surreal0,X1)|k4_surrealc(X1)=k2_surrealr(X1)|~v2_surreal0(X1)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_34, negated_conjecture, (~r1_surrealo(esk2_0,k8_surrealr(esk3_0,k4_surrealc(esk1_0)))|~r1_surrealo(k11_surreal0,esk3_0)|~r1_surrealo(k11_surreal0,esk2_0)|~v2_surreal0(k4_surrealc(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_17])])).
cnf(c_0_35, plain, (r1_surrealo(X1,k8_surrealr(X2,X3))|~r1_surrealo(k11_surreal0,X3)|~r1_surrealo(X1,X2)|~v2_surreal0(X3)|~v2_surreal0(X2)|~v2_surreal0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_29])])).
cnf(c_0_36, negated_conjecture, (r1_surrealo(esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_37, plain, ![X37]:(~v2_surreal0(X37)|r1_surrealo(k11_surreal0,k4_surrealc(X37))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t31_surrealc])])).
cnf(c_0_38, plain, (r5_surreal0(X1,X2)|~r5_surreal0(X1,X3)|~r1_surrealo(X3,X2)|~v2_surreal0(X2)|~v2_surreal0(X3)|~v2_surreal0(X1)), inference(spm,[status(thm)],[c_0_30, c_0_31])).
cnf(c_0_39, plain, (r1_surrealo(k2_surrealr(X2),k2_surrealr(X1))|~r1_surrealo(X1,X2)|~v2_surreal0(X2)|~v2_surreal0(X1)), inference(split_conjunct,[status(thm)],[c_0_32])).
cnf(c_0_40, negated_conjecture, (k2_surrealr(esk2_0)=k4_surrealc(esk2_0)|r1_surrealo(k11_surreal0,esk2_0)), inference(spm,[status(thm)],[c_0_33, c_0_19])).
cnf(c_0_41, negated_conjecture, (~r1_surrealo(k11_surreal0,k4_surrealc(esk1_0))|~r1_surrealo(k11_surreal0,esk3_0)|~r1_surrealo(k11_surreal0,esk2_0)|~v2_surreal0(k4_surrealc(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_36]), c_0_17]), c_0_19])])).
cnf(c_0_42, plain, (r1_surrealo(k11_surreal0,k4_surrealc(X1))|~v2_surreal0(X1)), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_43, negated_conjecture, (v2_surreal0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_44, plain, ![X31]:(~v2_surreal0(X31)|v2_surreal0(k4_surrealc(X31))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_surrealc])])).
cnf(c_0_45, plain, (r5_surreal0(X1,X2)|~r1_surrealo(X3,X2)|~r1_surrealo(X1,X3)|~v2_surreal0(X2)|~v2_surreal0(X3)|~v2_surreal0(X1)), inference(spm,[status(thm)],[c_0_38, c_0_31])).
cnf(c_0_46, negated_conjecture, (r1_surrealo(k4_surrealc(esk2_0),k2_surrealr(X1))|r1_surrealo(k11_surreal0,esk2_0)|~r1_surrealo(X1,esk2_0)|~v2_surreal0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_19])])).
cnf(c_0_47, negated_conjecture, (r1_surrealo(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_13])).
cnf(c_0_48, negated_conjecture, (~r1_surrealo(k11_surreal0,esk3_0)|~r1_surrealo(k11_surreal0,esk2_0)|~v2_surreal0(k4_surrealc(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_43])])).
cnf(c_0_49, plain, (v2_surreal0(k4_surrealc(X1))|~v2_surreal0(X1)), inference(split_conjunct,[status(thm)],[c_0_44])).
cnf(c_0_50, plain, (r1_surrealo(X1,X2)|~r5_surreal0(X1,X2)|~v2_surreal0(X1)|~v2_surreal0(X2)), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_51, negated_conjecture, (r5_surreal0(X1,esk3_0)|~r1_surrealo(X1,esk2_0)|~v2_surreal0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_36]), c_0_17]), c_0_19])])).
cnf(c_0_52, negated_conjecture, (r1_surrealo(k4_surrealc(esk2_0),k2_surrealr(esk1_0))|r1_surrealo(k11_surreal0,esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_43])])).
cnf(c_0_53, negated_conjecture, (k2_surrealr(esk1_0)=k4_surrealc(esk1_0)|r1_surrealo(k11_surreal0,esk1_0)), inference(spm,[status(thm)],[c_0_33, c_0_43])).
cnf(c_0_54, negated_conjecture, (~r1_surrealo(k11_surreal0,esk3_0)|~r1_surrealo(k11_surreal0,esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_43])])).
cnf(c_0_55, negated_conjecture, (r1_surrealo(X1,esk3_0)|~r1_surrealo(X1,esk2_0)|~v2_surreal0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_17])])).
cnf(c_0_56, negated_conjecture, (r1_surrealo(k4_surrealc(esk2_0),k4_surrealc(esk1_0))|r1_surrealo(k11_surreal0,esk1_0)|r1_surrealo(k11_surreal0,esk2_0)), inference(spm,[status(thm)],[c_0_52, c_0_53])).
cnf(c_0_57, negated_conjecture, (~r1_surrealo(k11_surreal0,esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_29])])).
cnf(c_0_58, negated_conjecture, (~r1_surrealo(k4_surrealc(esk2_0),k4_surrealc(esk1_0))|~r1_surrealo(k11_surreal0,k4_surrealc(esk3_0))|~v2_surreal0(k4_surrealc(esk3_0))|~v2_surreal0(k4_surrealc(esk1_0))|~v2_surreal0(k4_surrealc(esk2_0))), inference(spm,[status(thm)],[c_0_15, c_0_35])).
cnf(c_0_59, negated_conjecture, (r1_surrealo(k4_surrealc(esk2_0),k4_surrealc(esk1_0))|r1_surrealo(k11_surreal0,esk1_0)), inference(sr,[status(thm)],[c_0_56, c_0_57])).
cnf(c_0_60, negated_conjecture, (r1_surrealo(k11_surreal0,esk1_0)|~r1_surrealo(k11_surreal0,k4_surrealc(esk3_0))|~v2_surreal0(k4_surrealc(esk3_0))|~v2_surreal0(k4_surrealc(esk1_0))|~v2_surreal0(k4_surrealc(esk2_0))), inference(spm,[status(thm)],[c_0_58, c_0_59])).
cnf(c_0_61, negated_conjecture, (r1_surrealo(k11_surreal0,esk1_0)|~v2_surreal0(k4_surrealc(esk3_0))|~v2_surreal0(k4_surrealc(esk1_0))|~v2_surreal0(k4_surrealc(esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_42]), c_0_17])])).
cnf(c_0_62, negated_conjecture, (r1_surrealo(k11_surreal0,esk1_0)|~v2_surreal0(k4_surrealc(esk1_0))|~v2_surreal0(k4_surrealc(esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_49]), c_0_17])])).
cnf(c_0_63, negated_conjecture, (r5_surreal0(X1,esk2_0)|~r1_surrealo(X1,esk1_0)|~v2_surreal0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_47]), c_0_19]), c_0_43])])).
cnf(c_0_64, negated_conjecture, (r1_surrealo(k11_surreal0,esk1_0)|~v2_surreal0(k4_surrealc(esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_49]), c_0_43])])).
cnf(c_0_65, negated_conjecture, (r1_surrealo(X1,esk2_0)|~r1_surrealo(X1,esk1_0)|~v2_surreal0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_63]), c_0_19])])).
cnf(c_0_66, negated_conjecture, (r1_surrealo(k11_surreal0,esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_49]), c_0_19])])).
cnf(c_0_67, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_29])]), c_0_57]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 68
# Proof object clause steps            : 45
# Proof object formula steps           : 23
# Proof object conjectures             : 33
# Proof object clause conjectures      : 30
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 18
# Proof object initial formulas used   : 11
# Proof object generating inferences   : 26
# Proof object simplifying inferences  : 44
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 11
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 19
# Removed in clause preprocessing      : 0
# Initial clauses in saturation        : 19
# Processed clauses                    : 284
# ...of these trivial                  : 0
# ...subsumed                          : 108
# ...remaining for further processing  : 176
# Other redundant clauses eliminated   : 0
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 23
# Backward-rewritten                   : 30
# Generated clauses                    : 464
# ...of the previous two non-trivial   : 384
# Contextual simplify-reflections      : 1
# Paramodulations                      : 459
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 0
# Propositional unsat checks           : 0
#    Propositional check models        : 0
#    Propositional check unsatisfiable : 0
#    Propositional clauses             : 0
#    Propositional clauses after purity: 0
#    Propositional unsat core size     : 0
#    Propositional preprocessing time  : 0.000
#    Propositional encoding time       : 0.000
#    Propositional solver time         : 0.000
#    Success case prop preproc time    : 0.000
#    Success case prop encoding time   : 0.000
#    Success case prop solver time     : 0.000
# Current number of processed clauses  : 99
#    Positive orientable unit clauses  : 10
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 2
#    Non-unit-clauses                  : 87
# Current number of unprocessed clauses: 120
# ...number of literals in the above   : 798
# Current number of archived formulas  : 0
# Current number of archived clauses   : 77
# Clause-clause subsumption calls (NU) : 3054
# Rec. Clause-clause subsumption calls : 1100
# Non-unit clause-clause subsumptions  : 106
# Unit Clause-clause subsumption calls : 106
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 2
# BW rewrite match successes           : 2
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 9858

# -------------------------------------------------
# User time                : 0.031 s
# System time              : 0.002 s
# Total time               : 0.033 s
# Maximum resident set size: 3560 pages
