# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S053I
# and selection function HSelectMinInfpos.
#
# Preprocessing time       : 0.022 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t17_proofs_1, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>![X3]:(m1_proofs_1(X3,X1)=>![X4]:(r2_proofs_1(X2,X4,X3)=>r2_hidden(X4,X1))))), file('proofs_1/proofs_1__t17_proofs_1', t17_proofs_1)).
fof(dt_m1_proofs_1, axiom, ![X1, X2]:(m1_proofs_1(X2,X1)=>(v1_relat_1(X2)&v1_proofs_1(X2))), file('proofs_1/proofs_1__t17_proofs_1', dt_m1_proofs_1)).
fof(d10_proofs_1, axiom, ![X1, X2, X3]:((v1_relat_1(X3)&v1_proofs_1(X3))=>(r2_proofs_1(X1,X2,X3)<=>?[X4]:((((v1_relat_1(X4)&v1_funct_1(X4))&v1_finseq_1(X4))&r2_hidden(X2,k1_proofs_1(X4)))&v2_proofs_1(X4,X1,X3)))), file('proofs_1/proofs_1__t17_proofs_1', d10_proofs_1)).
fof(l38_proofs_1, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>![X3]:(m1_proofs_1(X3,X1)=>![X4]:((((v1_relat_1(X4)&v1_funct_1(X4))&v1_finseq_1(X4))&v2_proofs_1(X4,X2,X3))=>m4_proofs_1(X4,X1))))), file('proofs_1/proofs_1__t17_proofs_1', l38_proofs_1)).
fof(d5_proofs_1, axiom, ![X1, X2]:(((v1_relat_1(X2)&v1_funct_1(X2))&v1_finseq_1(X2))=>(m4_proofs_1(X2,X1)<=>m2_finseq_1(X2,X1))), file('proofs_1/proofs_1__t17_proofs_1', d5_proofs_1)).
fof(d4_finseq_1, axiom, ![X1, X2]:(((v1_relat_1(X2)&v1_funct_1(X2))&v1_finseq_1(X2))=>(m1_finseq_1(X2,X1)<=>r1_tarski(k10_xtuple_0(X2),X1))), file('proofs_1/proofs_1__t17_proofs_1', d4_finseq_1)).
fof(dt_m1_finseq_1, axiom, ![X1, X2]:(m1_finseq_1(X2,X1)=>((v1_relat_1(X2)&v1_funct_1(X2))&v1_finseq_1(X2))), file('proofs_1/proofs_1__t17_proofs_1', dt_m1_finseq_1)).
fof(redefinition_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)<=>m1_finseq_1(X2,X1)), file('proofs_1/proofs_1__t17_proofs_1', redefinition_m2_finseq_1)).
fof(redefinition_k1_proofs_1, axiom, ![X1]:(((v1_relat_1(X1)&v1_funct_1(X1))&v1_finseq_1(X1))=>k1_proofs_1(X1)=k10_xtuple_0(X1)), file('proofs_1/proofs_1__t17_proofs_1', redefinition_k1_proofs_1)).
fof(d3_tarski, axiom, ![X1, X2]:(r1_tarski(X1,X2)<=>![X3]:(r2_hidden(X3,X1)=>r2_hidden(X3,X2))), file('proofs_1/proofs_1__t17_proofs_1', d3_tarski)).
fof(c_0_10, negated_conjecture, ~(![X1]:(~v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>![X3]:(m1_proofs_1(X3,X1)=>![X4]:(r2_proofs_1(X2,X4,X3)=>r2_hidden(X4,X1)))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t17_proofs_1])])).
fof(c_0_11, plain, ![X52, X53]:((v1_relat_1(X53)|~m1_proofs_1(X53,X52))&(v1_proofs_1(X53)|~m1_proofs_1(X53,X52))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_proofs_1])])])).
fof(c_0_12, negated_conjecture, (~v1_xboole_0(esk1_0)&(m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0))&(m1_proofs_1(esk3_0,esk1_0)&(r2_proofs_1(esk2_0,esk4_0,esk3_0)&~r2_hidden(esk4_0,esk1_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])).
fof(c_0_13, plain, ![X35, X36, X37, X39]:((((((v1_relat_1(esk5_3(X35,X36,X37))|~r2_proofs_1(X35,X36,X37)|(~v1_relat_1(X37)|~v1_proofs_1(X37)))&(v1_funct_1(esk5_3(X35,X36,X37))|~r2_proofs_1(X35,X36,X37)|(~v1_relat_1(X37)|~v1_proofs_1(X37))))&(v1_finseq_1(esk5_3(X35,X36,X37))|~r2_proofs_1(X35,X36,X37)|(~v1_relat_1(X37)|~v1_proofs_1(X37))))&(r2_hidden(X36,k1_proofs_1(esk5_3(X35,X36,X37)))|~r2_proofs_1(X35,X36,X37)|(~v1_relat_1(X37)|~v1_proofs_1(X37))))&(v2_proofs_1(esk5_3(X35,X36,X37),X35,X37)|~r2_proofs_1(X35,X36,X37)|(~v1_relat_1(X37)|~v1_proofs_1(X37))))&(~v1_relat_1(X39)|~v1_funct_1(X39)|~v1_finseq_1(X39)|~r2_hidden(X36,k1_proofs_1(X39))|~v2_proofs_1(X39,X35,X37)|r2_proofs_1(X35,X36,X37)|(~v1_relat_1(X37)|~v1_proofs_1(X37)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_proofs_1])])])])])).
cnf(c_0_14, plain, (v1_proofs_1(X1)|~m1_proofs_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_11])).
cnf(c_0_15, negated_conjecture, (m1_proofs_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_16, plain, (v1_relat_1(X1)|~m1_proofs_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_11])).
fof(c_0_17, plain, ![X1]:(~v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>![X3]:(m1_proofs_1(X3,X1)=>![X4]:((((v1_relat_1(X4)&v1_funct_1(X4))&v1_finseq_1(X4))&v2_proofs_1(X4,X2,X3))=>m4_proofs_1(X4,X1))))), inference(fof_simplification,[status(thm)],[l38_proofs_1])).
cnf(c_0_18, plain, (v1_finseq_1(esk5_3(X1,X2,X3))|~r2_proofs_1(X1,X2,X3)|~v1_relat_1(X3)|~v1_proofs_1(X3)), inference(split_conjunct,[status(thm)],[c_0_13])).
cnf(c_0_19, negated_conjecture, (v1_proofs_1(esk3_0)), inference(spm,[status(thm)],[c_0_14, c_0_15])).
cnf(c_0_20, negated_conjecture, (v1_relat_1(esk3_0)), inference(spm,[status(thm)],[c_0_16, c_0_15])).
cnf(c_0_21, plain, (v1_funct_1(esk5_3(X1,X2,X3))|~r2_proofs_1(X1,X2,X3)|~v1_relat_1(X3)|~v1_proofs_1(X3)), inference(split_conjunct,[status(thm)],[c_0_13])).
cnf(c_0_22, plain, (v1_relat_1(esk5_3(X1,X2,X3))|~r2_proofs_1(X1,X2,X3)|~v1_relat_1(X3)|~v1_proofs_1(X3)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_23, plain, ![X54, X55, X56, X57]:(v1_xboole_0(X54)|(~m1_subset_1(X55,k1_zfmisc_1(X54))|(~m1_proofs_1(X56,X54)|(~v1_relat_1(X57)|~v1_funct_1(X57)|~v1_finseq_1(X57)|~v2_proofs_1(X57,X55,X56)|m4_proofs_1(X57,X54))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])).
cnf(c_0_24, negated_conjecture, (v1_finseq_1(esk5_3(X1,X2,esk3_0))|~r2_proofs_1(X1,X2,esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19]), c_0_20])])).
cnf(c_0_25, negated_conjecture, (r2_proofs_1(esk2_0,esk4_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_26, negated_conjecture, (v1_funct_1(esk5_3(X1,X2,esk3_0))|~r2_proofs_1(X1,X2,esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_19]), c_0_20])])).
cnf(c_0_27, negated_conjecture, (v1_relat_1(esk5_3(X1,X2,esk3_0))|~r2_proofs_1(X1,X2,esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_19]), c_0_20])])).
cnf(c_0_28, plain, (v1_xboole_0(X1)|m4_proofs_1(X4,X1)|~m1_subset_1(X2,k1_zfmisc_1(X1))|~m1_proofs_1(X3,X1)|~v1_relat_1(X4)|~v1_funct_1(X4)|~v1_finseq_1(X4)|~v2_proofs_1(X4,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_29, negated_conjecture, (v1_finseq_1(esk5_3(esk2_0,esk4_0,esk3_0))), inference(spm,[status(thm)],[c_0_24, c_0_25])).
cnf(c_0_30, negated_conjecture, (v1_funct_1(esk5_3(esk2_0,esk4_0,esk3_0))), inference(spm,[status(thm)],[c_0_26, c_0_25])).
cnf(c_0_31, negated_conjecture, (v1_relat_1(esk5_3(esk2_0,esk4_0,esk3_0))), inference(spm,[status(thm)],[c_0_27, c_0_25])).
cnf(c_0_32, plain, (v2_proofs_1(esk5_3(X1,X2,X3),X1,X3)|~r2_proofs_1(X1,X2,X3)|~v1_relat_1(X3)|~v1_proofs_1(X3)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_33, plain, ![X48, X49]:((~m4_proofs_1(X49,X48)|m2_finseq_1(X49,X48)|(~v1_relat_1(X49)|~v1_funct_1(X49)|~v1_finseq_1(X49)))&(~m2_finseq_1(X49,X48)|m4_proofs_1(X49,X48)|(~v1_relat_1(X49)|~v1_funct_1(X49)|~v1_finseq_1(X49)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_proofs_1])])])).
cnf(c_0_34, negated_conjecture, (m4_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0),X1)|v1_xboole_0(X1)|~v2_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0),X2,X3)|~m1_proofs_1(X3,X1)|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30]), c_0_31])])).
cnf(c_0_35, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_36, negated_conjecture, (v2_proofs_1(esk5_3(X1,X2,esk3_0),X1,esk3_0)|~r2_proofs_1(X1,X2,esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_19]), c_0_20])])).
cnf(c_0_37, plain, (m2_finseq_1(X1,X2)|~m4_proofs_1(X1,X2)|~v1_relat_1(X1)|~v1_funct_1(X1)|~v1_finseq_1(X1)), inference(split_conjunct,[status(thm)],[c_0_33])).
cnf(c_0_38, negated_conjecture, (m4_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0),esk1_0)|~v2_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0),X1,esk3_0)|~m1_subset_1(X1,k1_zfmisc_1(esk1_0))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_15]), c_0_35])).
cnf(c_0_39, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_40, negated_conjecture, (v2_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0),esk2_0,esk3_0)), inference(spm,[status(thm)],[c_0_36, c_0_25])).
fof(c_0_41, plain, ![X46, X47]:((~m1_finseq_1(X47,X46)|r1_tarski(k10_xtuple_0(X47),X46)|(~v1_relat_1(X47)|~v1_funct_1(X47)|~v1_finseq_1(X47)))&(~r1_tarski(k10_xtuple_0(X47),X46)|m1_finseq_1(X47,X46)|(~v1_relat_1(X47)|~v1_funct_1(X47)|~v1_finseq_1(X47)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_finseq_1])])])).
fof(c_0_42, plain, ![X50, X51]:(((v1_relat_1(X51)|~m1_finseq_1(X51,X50))&(v1_funct_1(X51)|~m1_finseq_1(X51,X50)))&(v1_finseq_1(X51)|~m1_finseq_1(X51,X50))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_finseq_1])])])).
fof(c_0_43, plain, ![X59, X60]:((~m2_finseq_1(X60,X59)|m1_finseq_1(X60,X59))&(~m1_finseq_1(X60,X59)|m2_finseq_1(X60,X59))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_finseq_1])])).
cnf(c_0_44, negated_conjecture, (m2_finseq_1(esk5_3(esk2_0,esk4_0,esk3_0),X1)|~m4_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0),X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_29]), c_0_30]), c_0_31])])).
cnf(c_0_45, negated_conjecture, (m4_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0),esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40])])).
cnf(c_0_46, plain, (r1_tarski(k10_xtuple_0(X1),X2)|~m1_finseq_1(X1,X2)|~v1_relat_1(X1)|~v1_funct_1(X1)|~v1_finseq_1(X1)), inference(split_conjunct,[status(thm)],[c_0_41])).
cnf(c_0_47, plain, (v1_relat_1(X1)|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_48, plain, (v1_funct_1(X1)|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_49, plain, (v1_finseq_1(X1)|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_42])).
cnf(c_0_50, plain, (m1_finseq_1(X1,X2)|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_43])).
cnf(c_0_51, negated_conjecture, (m2_finseq_1(esk5_3(esk2_0,esk4_0,esk3_0),esk1_0)), inference(spm,[status(thm)],[c_0_44, c_0_45])).
cnf(c_0_52, plain, (r2_hidden(X1,k1_proofs_1(esk5_3(X2,X1,X3)))|~r2_proofs_1(X2,X1,X3)|~v1_relat_1(X3)|~v1_proofs_1(X3)), inference(split_conjunct,[status(thm)],[c_0_13])).
fof(c_0_53, plain, ![X58]:(~v1_relat_1(X58)|~v1_funct_1(X58)|~v1_finseq_1(X58)|k1_proofs_1(X58)=k10_xtuple_0(X58)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_proofs_1])])).
fof(c_0_54, plain, ![X40, X41, X42, X43, X44]:((~r1_tarski(X40,X41)|(~r2_hidden(X42,X40)|r2_hidden(X42,X41)))&((r2_hidden(esk6_2(X43,X44),X43)|r1_tarski(X43,X44))&(~r2_hidden(esk6_2(X43,X44),X44)|r1_tarski(X43,X44)))), 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])])])])])])).
cnf(c_0_55, plain, (r1_tarski(k10_xtuple_0(X1),X2)|~m1_finseq_1(X1,X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_46, c_0_47]), c_0_48]), c_0_49])).
cnf(c_0_56, negated_conjecture, (m1_finseq_1(esk5_3(esk2_0,esk4_0,esk3_0),esk1_0)), inference(spm,[status(thm)],[c_0_50, c_0_51])).
cnf(c_0_57, negated_conjecture, (r2_hidden(X1,k1_proofs_1(esk5_3(X2,X1,esk3_0)))|~r2_proofs_1(X2,X1,esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_19]), c_0_20])])).
cnf(c_0_58, plain, (k1_proofs_1(X1)=k10_xtuple_0(X1)|~v1_relat_1(X1)|~v1_funct_1(X1)|~v1_finseq_1(X1)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_59, plain, (r2_hidden(X3,X2)|~r1_tarski(X1,X2)|~r2_hidden(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_54])).
cnf(c_0_60, negated_conjecture, (r1_tarski(k10_xtuple_0(esk5_3(esk2_0,esk4_0,esk3_0)),esk1_0)), inference(spm,[status(thm)],[c_0_55, c_0_56])).
cnf(c_0_61, negated_conjecture, (r2_hidden(esk4_0,k1_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0)))), inference(spm,[status(thm)],[c_0_57, c_0_25])).
cnf(c_0_62, negated_conjecture, (k1_proofs_1(esk5_3(esk2_0,esk4_0,esk3_0))=k10_xtuple_0(esk5_3(esk2_0,esk4_0,esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_29]), c_0_30]), c_0_31])])).
cnf(c_0_63, negated_conjecture, (r2_hidden(X1,esk1_0)|~r2_hidden(X1,k10_xtuple_0(esk5_3(esk2_0,esk4_0,esk3_0)))), inference(spm,[status(thm)],[c_0_59, c_0_60])).
cnf(c_0_64, negated_conjecture, (r2_hidden(esk4_0,k10_xtuple_0(esk5_3(esk2_0,esk4_0,esk3_0)))), inference(rw,[status(thm)],[c_0_61, c_0_62])).
cnf(c_0_65, negated_conjecture, (~r2_hidden(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_66, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64]), c_0_65]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 67
# Proof object clause steps            : 45
# Proof object formula steps           : 22
# Proof object conjectures             : 31
# Proof object clause conjectures      : 28
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 21
# Proof object initial formulas used   : 10
# Proof object generating inferences   : 22
# Proof object simplifying inferences  : 27
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 10
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 27
# Removed in clause preprocessing      : 0
# Initial clauses in saturation        : 27
# Processed clauses                    : 90
# ...of these trivial                  : 2
# ...subsumed                          : 0
# ...remaining for further processing  : 88
# Other redundant clauses eliminated   : 0
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 1
# Backward-rewritten                   : 1
# Generated clauses                    : 63
# ...of the previous two non-trivial   : 50
# Contextual simplify-reflections      : 3
# Paramodulations                      : 61
# Factorizations                       : 2
# 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  : 59
#    Positive orientable unit clauses  : 16
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 2
#    Non-unit-clauses                  : 41
# Current number of unprocessed clauses: 9
# ...number of literals in the above   : 20
# Current number of archived formulas  : 0
# Current number of archived clauses   : 29
# Clause-clause subsumption calls (NU) : 1074
# Rec. Clause-clause subsumption calls : 370
# Non-unit clause-clause subsumptions  : 3
# Unit Clause-clause subsumption calls : 8
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 3
# BW rewrite match successes           : 2
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 3631

# -------------------------------------------------
# User time                : 0.025 s
# System time              : 0.002 s
# Total time               : 0.027 s
# Maximum resident set size: 3556 pages
