# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___208_C18_F1_AE_CS_SP_PS_S0V
# and selection function PSelectComplexExceptRRHorn.
#
# Preprocessing time       : 0.022 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(fraenkel_a_2_1_field_16, axiom, ![X1, X2, X3]:(((((((((((v7_ordinal1(X2)&~(v2_struct_0(X3)))&v13_algstr_0(X3))&v2_rlvect_1(X3))&v3_rlvect_1(X3))&v4_rlvect_1(X3))&v4_vectsp_1(X3))&v5_vectsp_1(X3))&v3_group_1(X3))&v3_ring_3(X3,X2))&l6_algstr_0(X3))=>(r2_hidden(X1,a_2_1_field_16(X2,X3))<=>?[X4]:((m1_subset_1(X4,u1_struct_0(X3))&X1=X4)&k2_binom(X3,X4,X2)=k4_struct_0(X3)))), file('field_16/field_16__t21_field_16', fraenkel_a_2_1_field_16)).
fof(dt_k5_field_16, axiom, ![X1]:(((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>((v1_funct_1(k5_field_16(X1))&v1_funct_2(k5_field_16(X1),u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(k5_field_16(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))), file('field_16/field_16__t21_field_16', dt_k5_field_16)).
fof(t21_field_16, conjecture, ![X1]:(v7_ordinal1(X1)=>![X2]:((((((((((~(v2_struct_0(X2))&v13_algstr_0(X2))&v2_rlvect_1(X2))&v3_rlvect_1(X2))&v4_rlvect_1(X2))&v4_vectsp_1(X2))&v5_vectsp_1(X2))&v3_group_1(X2))&v3_ring_3(X2,X1))&l6_algstr_0(X2))=>k8_vectsp10(X2,X2,k5_field_16(X2))=a_2_1_field_16(X1,X2))), file('field_16/field_16__t21_field_16', t21_field_16)).
fof(t2_tarski, axiom, ![X1, X2]:(![X3]:(r2_hidden(X3,X1)<=>r2_hidden(X3,X2))=>X1=X2), file('field_16/field_16__t21_field_16', t2_tarski)).
fof(d9_vectsp10, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>![X2]:(l2_struct_0(X2)=>![X3]:(((v1_funct_1(X3)&v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2)))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2)))))=>k8_vectsp10(X1,X2,X3)=a_3_1_vectsp10(X1,X2,X3)))), file('field_16/field_16__t21_field_16', d9_vectsp10)).
fof(fraenkel_a_3_1_vectsp10, axiom, ![X1, X2, X3, X4]:((((((~(v2_struct_0(X2))&l1_struct_0(X2))&l2_struct_0(X3))&v1_funct_1(X4))&v1_funct_2(X4,u1_struct_0(X2),u1_struct_0(X3)))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X3)))))=>(r2_hidden(X1,a_3_1_vectsp10(X2,X3,X4))<=>?[X5]:((m1_subset_1(X5,u1_struct_0(X2))&X1=X5)&k3_funct_2(u1_struct_0(X2),u1_struct_0(X3),X4,X5)=k4_struct_0(X3)))), file('field_16/field_16__t21_field_16', fraenkel_a_3_1_vectsp10)).
fof(dt_l2_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>l1_struct_0(X1)), file('field_16/field_16__t21_field_16', dt_l2_struct_0)).
fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('field_16/field_16__t21_field_16', dt_l2_algstr_0)).
fof(dt_l6_algstr_0, axiom, ![X1]:(l6_algstr_0(X1)=>(l2_algstr_0(X1)&l5_algstr_0(X1))), file('field_16/field_16__t21_field_16', dt_l6_algstr_0)).
fof(d6_ring_3, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(((((((((~(v2_struct_0(X2))&v13_algstr_0(X2))&v3_group_1(X2))&v2_rlvect_1(X2))&v3_rlvect_1(X2))&v4_rlvect_1(X2))&v4_vectsp_1(X2))&v5_vectsp_1(X2))&l6_algstr_0(X2))=>(v3_ring_3(X2,X1)<=>k3_ring_3(X2)=X1))), file('field_16/field_16__t21_field_16', d6_ring_3)).
fof(d6_field_16, axiom, ![X1]:(((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>![X2]:(((v1_funct_1(X2)&v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))=>(X2=k5_field_16(X1)<=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),X2,X3)=k2_binom(X1,X3,k3_ring_3(X1)))))), file('field_16/field_16__t21_field_16', d6_field_16)).
fof(c_0_11, plain, ![X1, X2, X3]:(((((((((((v7_ordinal1(X2)&~v2_struct_0(X3))&v13_algstr_0(X3))&v2_rlvect_1(X3))&v3_rlvect_1(X3))&v4_rlvect_1(X3))&v4_vectsp_1(X3))&v5_vectsp_1(X3))&v3_group_1(X3))&v3_ring_3(X3,X2))&l6_algstr_0(X3))=>(r2_hidden(X1,a_2_1_field_16(X2,X3))<=>?[X4]:((m1_subset_1(X4,u1_struct_0(X3))&X1=X4)&k2_binom(X3,X4,X2)=k4_struct_0(X3)))), inference(fof_simplification,[status(thm)],[fraenkel_a_2_1_field_16])).
fof(c_0_12, plain, ![X1]:(((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>((v1_funct_1(k5_field_16(X1))&v1_funct_2(k5_field_16(X1),u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(k5_field_16(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))), inference(fof_simplification,[status(thm)],[dt_k5_field_16])).
fof(c_0_13, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>![X2]:((((((((((~v2_struct_0(X2)&v13_algstr_0(X2))&v2_rlvect_1(X2))&v3_rlvect_1(X2))&v4_rlvect_1(X2))&v4_vectsp_1(X2))&v5_vectsp_1(X2))&v3_group_1(X2))&v3_ring_3(X2,X1))&l6_algstr_0(X2))=>k8_vectsp10(X2,X2,k5_field_16(X2))=a_2_1_field_16(X1,X2)))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t21_field_16])])).
fof(c_0_14, plain, ![X47, X48, X49, X51]:((((m1_subset_1(esk4_3(X47,X48,X49),u1_struct_0(X49))|~r2_hidden(X47,a_2_1_field_16(X48,X49))|(~v7_ordinal1(X48)|v2_struct_0(X49)|~v13_algstr_0(X49)|~v2_rlvect_1(X49)|~v3_rlvect_1(X49)|~v4_rlvect_1(X49)|~v4_vectsp_1(X49)|~v5_vectsp_1(X49)|~v3_group_1(X49)|~v3_ring_3(X49,X48)|~l6_algstr_0(X49)))&(X47=esk4_3(X47,X48,X49)|~r2_hidden(X47,a_2_1_field_16(X48,X49))|(~v7_ordinal1(X48)|v2_struct_0(X49)|~v13_algstr_0(X49)|~v2_rlvect_1(X49)|~v3_rlvect_1(X49)|~v4_rlvect_1(X49)|~v4_vectsp_1(X49)|~v5_vectsp_1(X49)|~v3_group_1(X49)|~v3_ring_3(X49,X48)|~l6_algstr_0(X49))))&(k2_binom(X49,esk4_3(X47,X48,X49),X48)=k4_struct_0(X49)|~r2_hidden(X47,a_2_1_field_16(X48,X49))|(~v7_ordinal1(X48)|v2_struct_0(X49)|~v13_algstr_0(X49)|~v2_rlvect_1(X49)|~v3_rlvect_1(X49)|~v4_rlvect_1(X49)|~v4_vectsp_1(X49)|~v5_vectsp_1(X49)|~v3_group_1(X49)|~v3_ring_3(X49,X48)|~l6_algstr_0(X49))))&(~m1_subset_1(X51,u1_struct_0(X49))|X47!=X51|k2_binom(X49,X51,X48)!=k4_struct_0(X49)|r2_hidden(X47,a_2_1_field_16(X48,X49))|(~v7_ordinal1(X48)|v2_struct_0(X49)|~v13_algstr_0(X49)|~v2_rlvect_1(X49)|~v3_rlvect_1(X49)|~v4_rlvect_1(X49)|~v4_vectsp_1(X49)|~v5_vectsp_1(X49)|~v3_group_1(X49)|~v3_ring_3(X49,X48)|~l6_algstr_0(X49)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])).
fof(c_0_15, plain, ![X58, X59]:((~r2_hidden(esk6_2(X58,X59),X58)|~r2_hidden(esk6_2(X58,X59),X59)|X58=X59)&(r2_hidden(esk6_2(X58,X59),X58)|r2_hidden(esk6_2(X58,X59),X59)|X58=X59)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])).
fof(c_0_16, plain, ![X1]:((~v2_struct_0(X1)&l1_struct_0(X1))=>![X2]:(l2_struct_0(X2)=>![X3]:(((v1_funct_1(X3)&v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2)))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2)))))=>k8_vectsp10(X1,X2,X3)=a_3_1_vectsp10(X1,X2,X3)))), inference(fof_simplification,[status(thm)],[d9_vectsp10])).
fof(c_0_17, plain, ![X43]:(((v1_funct_1(k5_field_16(X43))|(v2_struct_0(X43)|~v13_algstr_0(X43)|~v2_rlvect_1(X43)|~v3_rlvect_1(X43)|~v4_rlvect_1(X43)|~v4_vectsp_1(X43)|~v5_vectsp_1(X43)|~v3_group_1(X43)|~l6_algstr_0(X43)))&(v1_funct_2(k5_field_16(X43),u1_struct_0(X43),u1_struct_0(X43))|(v2_struct_0(X43)|~v13_algstr_0(X43)|~v2_rlvect_1(X43)|~v3_rlvect_1(X43)|~v4_rlvect_1(X43)|~v4_vectsp_1(X43)|~v5_vectsp_1(X43)|~v3_group_1(X43)|~l6_algstr_0(X43))))&(m1_subset_1(k5_field_16(X43),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X43),u1_struct_0(X43))))|(v2_struct_0(X43)|~v13_algstr_0(X43)|~v2_rlvect_1(X43)|~v3_rlvect_1(X43)|~v4_rlvect_1(X43)|~v4_vectsp_1(X43)|~v5_vectsp_1(X43)|~v3_group_1(X43)|~l6_algstr_0(X43)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])).
fof(c_0_18, negated_conjecture, (v7_ordinal1(esk1_0)&((((((((((~v2_struct_0(esk2_0)&v13_algstr_0(esk2_0))&v2_rlvect_1(esk2_0))&v3_rlvect_1(esk2_0))&v4_rlvect_1(esk2_0))&v4_vectsp_1(esk2_0))&v5_vectsp_1(esk2_0))&v3_group_1(esk2_0))&v3_ring_3(esk2_0,esk1_0))&l6_algstr_0(esk2_0))&k8_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))!=a_2_1_field_16(esk1_0,esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])).
fof(c_0_19, plain, ![X1, X2, X3, X4]:((((((~v2_struct_0(X2)&l1_struct_0(X2))&l2_struct_0(X3))&v1_funct_1(X4))&v1_funct_2(X4,u1_struct_0(X2),u1_struct_0(X3)))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X3)))))=>(r2_hidden(X1,a_3_1_vectsp10(X2,X3,X4))<=>?[X5]:((m1_subset_1(X5,u1_struct_0(X2))&X1=X5)&k3_funct_2(u1_struct_0(X2),u1_struct_0(X3),X4,X5)=k4_struct_0(X3)))), inference(fof_simplification,[status(thm)],[fraenkel_a_3_1_vectsp10])).
cnf(c_0_20, plain, (X1=esk4_3(X1,X2,X3)|v2_struct_0(X3)|~r2_hidden(X1,a_2_1_field_16(X2,X3))|~v7_ordinal1(X2)|~v13_algstr_0(X3)|~v2_rlvect_1(X3)|~v3_rlvect_1(X3)|~v4_rlvect_1(X3)|~v4_vectsp_1(X3)|~v5_vectsp_1(X3)|~v3_group_1(X3)|~v3_ring_3(X3,X2)|~l6_algstr_0(X3)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_21, plain, (r2_hidden(esk6_2(X1,X2),X1)|r2_hidden(esk6_2(X1,X2),X2)|X1=X2), inference(split_conjunct,[status(thm)],[c_0_15])).
fof(c_0_22, plain, ![X40, X41, X42]:(v2_struct_0(X40)|~l1_struct_0(X40)|(~l2_struct_0(X41)|(~v1_funct_1(X42)|~v1_funct_2(X42,u1_struct_0(X40),u1_struct_0(X41))|~m1_subset_1(X42,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X40),u1_struct_0(X41))))|k8_vectsp10(X40,X41,X42)=a_3_1_vectsp10(X40,X41,X42)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])).
cnf(c_0_23, plain, (m1_subset_1(k5_field_16(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_24, negated_conjecture, (l6_algstr_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_25, negated_conjecture, (v3_group_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_26, negated_conjecture, (v5_vectsp_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_27, negated_conjecture, (v4_vectsp_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_28, negated_conjecture, (v4_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_29, negated_conjecture, (v3_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_30, negated_conjecture, (v2_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_31, negated_conjecture, (v13_algstr_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_32, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_33, plain, (v1_funct_2(k5_field_16(X1),u1_struct_0(X1),u1_struct_0(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_17])).
cnf(c_0_34, plain, (v1_funct_1(k5_field_16(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_17])).
fof(c_0_35, plain, ![X45]:(~l2_struct_0(X45)|l1_struct_0(X45)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])).
fof(c_0_36, plain, ![X52, X53, X54, X55, X57]:((((m1_subset_1(esk5_4(X52,X53,X54,X55),u1_struct_0(X53))|~r2_hidden(X52,a_3_1_vectsp10(X53,X54,X55))|(v2_struct_0(X53)|~l1_struct_0(X53)|~l2_struct_0(X54)|~v1_funct_1(X55)|~v1_funct_2(X55,u1_struct_0(X53),u1_struct_0(X54))|~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X53),u1_struct_0(X54))))))&(X52=esk5_4(X52,X53,X54,X55)|~r2_hidden(X52,a_3_1_vectsp10(X53,X54,X55))|(v2_struct_0(X53)|~l1_struct_0(X53)|~l2_struct_0(X54)|~v1_funct_1(X55)|~v1_funct_2(X55,u1_struct_0(X53),u1_struct_0(X54))|~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X53),u1_struct_0(X54)))))))&(k3_funct_2(u1_struct_0(X53),u1_struct_0(X54),X55,esk5_4(X52,X53,X54,X55))=k4_struct_0(X54)|~r2_hidden(X52,a_3_1_vectsp10(X53,X54,X55))|(v2_struct_0(X53)|~l1_struct_0(X53)|~l2_struct_0(X54)|~v1_funct_1(X55)|~v1_funct_2(X55,u1_struct_0(X53),u1_struct_0(X54))|~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X53),u1_struct_0(X54)))))))&(~m1_subset_1(X57,u1_struct_0(X53))|X52!=X57|k3_funct_2(u1_struct_0(X53),u1_struct_0(X54),X55,X57)!=k4_struct_0(X54)|r2_hidden(X52,a_3_1_vectsp10(X53,X54,X55))|(v2_struct_0(X53)|~l1_struct_0(X53)|~l2_struct_0(X54)|~v1_funct_1(X55)|~v1_funct_2(X55,u1_struct_0(X53),u1_struct_0(X54))|~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X53),u1_struct_0(X54))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])).
cnf(c_0_37, plain, (m1_subset_1(esk4_3(X1,X2,X3),u1_struct_0(X3))|v2_struct_0(X3)|~r2_hidden(X1,a_2_1_field_16(X2,X3))|~v7_ordinal1(X2)|~v13_algstr_0(X3)|~v2_rlvect_1(X3)|~v3_rlvect_1(X3)|~v4_rlvect_1(X3)|~v4_vectsp_1(X3)|~v5_vectsp_1(X3)|~v3_group_1(X3)|~v3_ring_3(X3,X2)|~l6_algstr_0(X3)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_38, plain, (esk4_3(esk6_2(a_2_1_field_16(X1,X2),X3),X1,X2)=esk6_2(a_2_1_field_16(X1,X2),X3)|a_2_1_field_16(X1,X2)=X3|r2_hidden(esk6_2(a_2_1_field_16(X1,X2),X3),X3)|v2_struct_0(X2)|~l6_algstr_0(X2)|~v3_ring_3(X2,X1)|~v3_group_1(X2)|~v5_vectsp_1(X2)|~v4_vectsp_1(X2)|~v4_rlvect_1(X2)|~v3_rlvect_1(X2)|~v2_rlvect_1(X2)|~v13_algstr_0(X2)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_20, c_0_21])).
cnf(c_0_39, negated_conjecture, (v3_ring_3(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_40, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_41, plain, (v2_struct_0(X1)|k8_vectsp10(X1,X2,X3)=a_3_1_vectsp10(X1,X2,X3)|~l1_struct_0(X1)|~l2_struct_0(X2)|~v1_funct_1(X3)|~v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2))))), inference(split_conjunct,[status(thm)],[c_0_22])).
cnf(c_0_42, negated_conjecture, (m1_subset_1(k5_field_16(esk2_0),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(esk2_0),u1_struct_0(esk2_0))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])).
cnf(c_0_43, negated_conjecture, (v1_funct_2(k5_field_16(esk2_0),u1_struct_0(esk2_0),u1_struct_0(esk2_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])).
cnf(c_0_44, negated_conjecture, (v1_funct_1(k5_field_16(esk2_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])).
cnf(c_0_45, plain, (l1_struct_0(X1)|~l2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_35])).
cnf(c_0_46, plain, (X1=esk5_4(X1,X2,X3,X4)|v2_struct_0(X2)|~r2_hidden(X1,a_3_1_vectsp10(X2,X3,X4))|~l1_struct_0(X2)|~l2_struct_0(X3)|~v1_funct_1(X4)|~v1_funct_2(X4,u1_struct_0(X2),u1_struct_0(X3))|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X3))))), inference(split_conjunct,[status(thm)],[c_0_36])).
cnf(c_0_47, plain, (a_2_1_field_16(X1,X2)=X3|r2_hidden(esk6_2(a_2_1_field_16(X1,X2),X3),X3)|m1_subset_1(esk4_3(esk6_2(a_2_1_field_16(X1,X2),X3),X1,X2),u1_struct_0(X2))|v2_struct_0(X2)|~l6_algstr_0(X2)|~v3_ring_3(X2,X1)|~v3_group_1(X2)|~v5_vectsp_1(X2)|~v4_vectsp_1(X2)|~v4_rlvect_1(X2)|~v3_rlvect_1(X2)|~v2_rlvect_1(X2)|~v13_algstr_0(X2)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_37, c_0_21])).
cnf(c_0_48, negated_conjecture, (esk4_3(esk6_2(a_2_1_field_16(esk1_0,esk2_0),X1),esk1_0,esk2_0)=esk6_2(a_2_1_field_16(esk1_0,esk2_0),X1)|a_2_1_field_16(esk1_0,esk2_0)=X1|r2_hidden(esk6_2(a_2_1_field_16(esk1_0,esk2_0),X1),X1)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_40])]), c_0_32])).
cnf(c_0_49, negated_conjecture, (k8_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))!=a_2_1_field_16(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_50, negated_conjecture, (k8_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))=a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_43]), c_0_44])]), c_0_32]), c_0_45])).
fof(c_0_51, plain, ![X44]:((l2_struct_0(X44)|~l2_algstr_0(X44))&(l1_algstr_0(X44)|~l2_algstr_0(X44))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])).
fof(c_0_52, plain, ![X46]:((l2_algstr_0(X46)|~l6_algstr_0(X46))&(l5_algstr_0(X46)|~l6_algstr_0(X46))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])).
cnf(c_0_53, negated_conjecture, (esk5_4(X1,esk2_0,esk2_0,k5_field_16(esk2_0))=X1|~r2_hidden(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_42]), c_0_43]), c_0_44])]), c_0_32]), c_0_45])).
cnf(c_0_54, negated_conjecture, (a_2_1_field_16(esk1_0,esk2_0)=X1|r2_hidden(esk6_2(a_2_1_field_16(esk1_0,esk2_0),X1),X1)|m1_subset_1(esk6_2(a_2_1_field_16(esk1_0,esk2_0),X1),u1_struct_0(esk2_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_24]), c_0_39]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_40])]), c_0_32])).
cnf(c_0_55, negated_conjecture, (a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))!=a_2_1_field_16(esk1_0,esk2_0)|~l2_struct_0(esk2_0)), inference(spm,[status(thm)],[c_0_49, c_0_50])).
cnf(c_0_56, plain, (l2_struct_0(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_51])).
cnf(c_0_57, plain, (l2_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_52])).
fof(c_0_58, plain, ![X1]:(v7_ordinal1(X1)=>![X2]:(((((((((~v2_struct_0(X2)&v13_algstr_0(X2))&v3_group_1(X2))&v2_rlvect_1(X2))&v3_rlvect_1(X2))&v4_rlvect_1(X2))&v4_vectsp_1(X2))&v5_vectsp_1(X2))&l6_algstr_0(X2))=>(v3_ring_3(X2,X1)<=>k3_ring_3(X2)=X1))), inference(fof_simplification,[status(thm)],[d6_ring_3])).
cnf(c_0_59, plain, (m1_subset_1(esk5_4(X1,X2,X3,X4),u1_struct_0(X2))|v2_struct_0(X2)|~r2_hidden(X1,a_3_1_vectsp10(X2,X3,X4))|~l1_struct_0(X2)|~l2_struct_0(X3)|~v1_funct_1(X4)|~v1_funct_2(X4,u1_struct_0(X2),u1_struct_0(X3))|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X3))))), inference(split_conjunct,[status(thm)],[c_0_36])).
cnf(c_0_60, negated_conjecture, (esk5_4(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|m1_subset_1(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),u1_struct_0(esk2_0))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_55])).
cnf(c_0_61, plain, (l2_struct_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_56, c_0_57])).
fof(c_0_62, plain, ![X1]:(((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>![X2]:(((v1_funct_1(X2)&v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))=>(X2=k5_field_16(X1)<=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),X2,X3)=k2_binom(X1,X3,k3_ring_3(X1)))))), inference(fof_simplification,[status(thm)],[d6_field_16])).
fof(c_0_63, plain, ![X38, X39]:((~v3_ring_3(X39,X38)|k3_ring_3(X39)=X38|(v2_struct_0(X39)|~v13_algstr_0(X39)|~v3_group_1(X39)|~v2_rlvect_1(X39)|~v3_rlvect_1(X39)|~v4_rlvect_1(X39)|~v4_vectsp_1(X39)|~v5_vectsp_1(X39)|~l6_algstr_0(X39))|~v7_ordinal1(X38))&(k3_ring_3(X39)!=X38|v3_ring_3(X39,X38)|(v2_struct_0(X39)|~v13_algstr_0(X39)|~v3_group_1(X39)|~v2_rlvect_1(X39)|~v3_rlvect_1(X39)|~v4_rlvect_1(X39)|~v4_vectsp_1(X39)|~v5_vectsp_1(X39)|~l6_algstr_0(X39))|~v7_ordinal1(X38))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])])).
cnf(c_0_64, negated_conjecture, (m1_subset_1(esk5_4(X1,esk2_0,esk2_0,k5_field_16(esk2_0)),u1_struct_0(esk2_0))|~r2_hidden(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_42]), c_0_43]), c_0_44])]), c_0_32]), c_0_45])).
cnf(c_0_65, negated_conjecture, (esk5_4(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|m1_subset_1(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),u1_struct_0(esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61]), c_0_24])])).
fof(c_0_66, plain, ![X34, X35, X36]:((X35!=k5_field_16(X34)|(~m1_subset_1(X36,u1_struct_0(X34))|k3_funct_2(u1_struct_0(X34),u1_struct_0(X34),X35,X36)=k2_binom(X34,X36,k3_ring_3(X34)))|(~v1_funct_1(X35)|~v1_funct_2(X35,u1_struct_0(X34),u1_struct_0(X34))|~m1_subset_1(X35,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X34),u1_struct_0(X34)))))|(v2_struct_0(X34)|~v13_algstr_0(X34)|~v2_rlvect_1(X34)|~v3_rlvect_1(X34)|~v4_rlvect_1(X34)|~v4_vectsp_1(X34)|~v5_vectsp_1(X34)|~v3_group_1(X34)|~l6_algstr_0(X34)))&((m1_subset_1(esk3_2(X34,X35),u1_struct_0(X34))|X35=k5_field_16(X34)|(~v1_funct_1(X35)|~v1_funct_2(X35,u1_struct_0(X34),u1_struct_0(X34))|~m1_subset_1(X35,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X34),u1_struct_0(X34)))))|(v2_struct_0(X34)|~v13_algstr_0(X34)|~v2_rlvect_1(X34)|~v3_rlvect_1(X34)|~v4_rlvect_1(X34)|~v4_vectsp_1(X34)|~v5_vectsp_1(X34)|~v3_group_1(X34)|~l6_algstr_0(X34)))&(k3_funct_2(u1_struct_0(X34),u1_struct_0(X34),X35,esk3_2(X34,X35))!=k2_binom(X34,esk3_2(X34,X35),k3_ring_3(X34))|X35=k5_field_16(X34)|(~v1_funct_1(X35)|~v1_funct_2(X35,u1_struct_0(X34),u1_struct_0(X34))|~m1_subset_1(X35,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X34),u1_struct_0(X34)))))|(v2_struct_0(X34)|~v13_algstr_0(X34)|~v2_rlvect_1(X34)|~v3_rlvect_1(X34)|~v4_rlvect_1(X34)|~v4_vectsp_1(X34)|~v5_vectsp_1(X34)|~v3_group_1(X34)|~l6_algstr_0(X34))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])])])).
cnf(c_0_67, plain, (k3_ring_3(X1)=X2|v2_struct_0(X1)|~v3_ring_3(X1,X2)|~v13_algstr_0(X1)|~v3_group_1(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_63])).
cnf(c_0_68, plain, (r2_hidden(X3,a_2_1_field_16(X4,X2))|v2_struct_0(X2)|~m1_subset_1(X1,u1_struct_0(X2))|X3!=X1|k2_binom(X2,X1,X4)!=k4_struct_0(X2)|~v7_ordinal1(X4)|~v13_algstr_0(X2)|~v2_rlvect_1(X2)|~v3_rlvect_1(X2)|~v4_rlvect_1(X2)|~v4_vectsp_1(X2)|~v5_vectsp_1(X2)|~v3_group_1(X2)|~v3_ring_3(X2,X4)|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_69, negated_conjecture, (m1_subset_1(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),u1_struct_0(esk2_0))|~r2_hidden(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(spm,[status(thm)],[c_0_64, c_0_65])).
cnf(c_0_70, plain, (k3_funct_2(u1_struct_0(X1),u1_struct_0(X2),X3,esk5_4(X4,X1,X2,X3))=k4_struct_0(X2)|v2_struct_0(X1)|~r2_hidden(X4,a_3_1_vectsp10(X1,X2,X3))|~l1_struct_0(X1)|~l2_struct_0(X2)|~v1_funct_1(X3)|~v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2))))), inference(split_conjunct,[status(thm)],[c_0_36])).
cnf(c_0_71, plain, (k3_funct_2(u1_struct_0(X2),u1_struct_0(X2),X1,X3)=k2_binom(X2,X3,k3_ring_3(X2))|v2_struct_0(X2)|X1!=k5_field_16(X2)|~m1_subset_1(X3,u1_struct_0(X2))|~v1_funct_1(X1)|~v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2))))|~v13_algstr_0(X2)|~v2_rlvect_1(X2)|~v3_rlvect_1(X2)|~v4_rlvect_1(X2)|~v4_vectsp_1(X2)|~v5_vectsp_1(X2)|~v3_group_1(X2)|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_66])).
cnf(c_0_72, negated_conjecture, (k3_ring_3(esk2_0)=esk1_0), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_39]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_40])]), c_0_32])).
cnf(c_0_73, plain, (X1=X2|~r2_hidden(esk6_2(X1,X2),X1)|~r2_hidden(esk6_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_15])).
cnf(c_0_74, plain, (r2_hidden(X1,a_2_1_field_16(X2,X3))|v2_struct_0(X3)|k2_binom(X3,X1,X2)!=k4_struct_0(X3)|~m1_subset_1(X1,u1_struct_0(X3))|~l6_algstr_0(X3)|~v3_ring_3(X3,X2)|~v3_group_1(X3)|~v5_vectsp_1(X3)|~v4_vectsp_1(X3)|~v4_rlvect_1(X3)|~v3_rlvect_1(X3)|~v2_rlvect_1(X3)|~v13_algstr_0(X3)|~v7_ordinal1(X2)), inference(er,[status(thm)],[c_0_68])).
cnf(c_0_75, negated_conjecture, (m1_subset_1(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),u1_struct_0(esk2_0))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_54]), c_0_55])).
cnf(c_0_76, negated_conjecture, (k3_funct_2(u1_struct_0(esk2_0),u1_struct_0(esk2_0),k5_field_16(esk2_0),esk5_4(X1,esk2_0,esk2_0,k5_field_16(esk2_0)))=k4_struct_0(esk2_0)|~r2_hidden(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_42]), c_0_43]), c_0_44])]), c_0_32]), c_0_45])).
cnf(c_0_77, negated_conjecture, (k3_funct_2(u1_struct_0(esk2_0),u1_struct_0(esk2_0),k5_field_16(esk2_0),X1)=k2_binom(esk2_0,X1,esk1_0)|~m1_subset_1(X1,u1_struct_0(esk2_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_42]), c_0_72]), c_0_43]), c_0_44]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])).
cnf(c_0_78, negated_conjecture, (esk5_4(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|esk4_3(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0,esk2_0)=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_48]), c_0_55])).
cnf(c_0_79, negated_conjecture, (esk4_3(esk6_2(a_2_1_field_16(esk1_0,esk2_0),X1),esk1_0,esk2_0)=esk6_2(a_2_1_field_16(esk1_0,esk2_0),X1)|a_2_1_field_16(esk1_0,esk2_0)=X1|~r2_hidden(esk6_2(a_2_1_field_16(esk1_0,esk2_0),X1),a_2_1_field_16(esk1_0,esk2_0))), inference(spm,[status(thm)],[c_0_73, c_0_48])).
cnf(c_0_80, negated_conjecture, (r2_hidden(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),a_2_1_field_16(X1,esk2_0))|k2_binom(esk2_0,esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),X1)!=k4_struct_0(esk2_0)|~l2_struct_0(esk2_0)|~v3_ring_3(esk2_0,X1)|~v7_ordinal1(X1)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])).
cnf(c_0_81, negated_conjecture, (esk5_4(esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|X1=a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))|r2_hidden(esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),X1)|~l2_struct_0(esk2_0)), inference(spm,[status(thm)],[c_0_53, c_0_21])).
cnf(c_0_82, negated_conjecture, (k2_binom(esk2_0,esk5_4(X1,esk2_0,esk2_0,k5_field_16(esk2_0)),esk1_0)=k4_struct_0(esk2_0)|~r2_hidden(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77]), c_0_64])).
cnf(c_0_83, negated_conjecture, (esk5_4(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|esk4_3(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0,esk2_0)=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_61]), c_0_24])])).
cnf(c_0_84, negated_conjecture, (esk4_3(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0,esk2_0)=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|k2_binom(esk2_0,esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0)!=k4_struct_0(esk2_0)|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80]), c_0_39]), c_0_40])]), c_0_55])).
cnf(c_0_85, plain, (k2_binom(X1,esk4_3(X2,X3,X1),X3)=k4_struct_0(X1)|v2_struct_0(X1)|~r2_hidden(X2,a_2_1_field_16(X3,X1))|~v7_ordinal1(X3)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~v3_ring_3(X1,X3)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_86, negated_conjecture, (esk5_4(esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|X1=a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))|r2_hidden(esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_61]), c_0_24])])).
cnf(c_0_87, negated_conjecture, (esk4_3(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0,esk2_0)=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~r2_hidden(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_84])).
cnf(c_0_88, plain, (r2_hidden(X3,a_3_1_vectsp10(X2,X4,X5))|v2_struct_0(X2)|~m1_subset_1(X1,u1_struct_0(X2))|X3!=X1|k3_funct_2(u1_struct_0(X2),u1_struct_0(X4),X5,X1)!=k4_struct_0(X4)|~l1_struct_0(X2)|~l2_struct_0(X4)|~v1_funct_1(X5)|~v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X4))|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X4))))), inference(split_conjunct,[status(thm)],[c_0_36])).
cnf(c_0_89, negated_conjecture, (esk5_4(esk6_2(a_2_1_field_16(X1,X2),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(a_2_1_field_16(X1,X2),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|k2_binom(X2,esk4_3(esk6_2(a_2_1_field_16(X1,X2),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),X1,X2),X1)=k4_struct_0(X2)|a_2_1_field_16(X1,X2)=a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))|v2_struct_0(X2)|~l6_algstr_0(X2)|~v3_ring_3(X2,X1)|~v3_group_1(X2)|~v5_vectsp_1(X2)|~v4_vectsp_1(X2)|~v4_rlvect_1(X2)|~v3_rlvect_1(X2)|~v2_rlvect_1(X2)|~v13_algstr_0(X2)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_85, c_0_86])).
cnf(c_0_90, negated_conjecture, (esk4_3(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0,esk2_0)=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_48]), c_0_55])).
cnf(c_0_91, plain, (r2_hidden(X1,a_3_1_vectsp10(X2,X3,X4))|v2_struct_0(X2)|k3_funct_2(u1_struct_0(X2),u1_struct_0(X3),X4,X1)!=k4_struct_0(X3)|~l2_struct_0(X3)|~l1_struct_0(X2)|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X3))))|~m1_subset_1(X1,u1_struct_0(X2))|~v1_funct_2(X4,u1_struct_0(X2),u1_struct_0(X3))|~v1_funct_1(X4)), inference(er,[status(thm)],[c_0_88])).
cnf(c_0_92, negated_conjecture, (esk5_4(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|k2_binom(esk2_0,esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0)=k4_struct_0(esk2_0)|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90]), c_0_24]), c_0_39]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_40])]), c_0_32]), c_0_55])).
cnf(c_0_93, negated_conjecture, (r2_hidden(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|k3_funct_2(u1_struct_0(esk2_0),u1_struct_0(esk2_0),k5_field_16(esk2_0),X1)!=k4_struct_0(esk2_0)|~l2_struct_0(esk2_0)|~m1_subset_1(X1,u1_struct_0(esk2_0))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_42]), c_0_43]), c_0_44])]), c_0_32]), c_0_45])).
cnf(c_0_94, negated_conjecture, (esk5_4(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk2_0,esk2_0,k5_field_16(esk2_0))=esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|k2_binom(esk2_0,esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0)=k4_struct_0(esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_61]), c_0_24])])).
cnf(c_0_95, negated_conjecture, (X1=a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))|k3_funct_2(u1_struct_0(esk2_0),u1_struct_0(esk2_0),k5_field_16(esk2_0),esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))))!=k4_struct_0(esk2_0)|~r2_hidden(esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),X1)|~l2_struct_0(esk2_0)|~m1_subset_1(esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),u1_struct_0(esk2_0))), inference(spm,[status(thm)],[c_0_73, c_0_93])).
cnf(c_0_96, negated_conjecture, (k2_binom(esk2_0,esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0)=k4_struct_0(esk2_0)|~r2_hidden(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0)))|~l2_struct_0(esk2_0)), inference(spm,[status(thm)],[c_0_82, c_0_94])).
cnf(c_0_97, negated_conjecture, (k2_binom(esk2_0,esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0)=k4_struct_0(esk2_0)|~r2_hidden(esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),a_2_1_field_16(esk1_0,esk2_0))|~l2_struct_0(esk2_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_90]), c_0_24]), c_0_39]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_40])]), c_0_32])).
cnf(c_0_98, negated_conjecture, (X1=a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))|k2_binom(esk2_0,esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0)!=k4_struct_0(esk2_0)|~r2_hidden(esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),X1)|~l2_struct_0(esk2_0)|~m1_subset_1(esk6_2(X1,a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),u1_struct_0(esk2_0))), inference(spm,[status(thm)],[c_0_95, c_0_77])).
cnf(c_0_99, negated_conjecture, (k2_binom(esk2_0,esk6_2(a_2_1_field_16(esk1_0,esk2_0),a_3_1_vectsp10(esk2_0,esk2_0,k5_field_16(esk2_0))),esk1_0)=k4_struct_0(esk2_0)|~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_21]), c_0_97]), c_0_55])).
cnf(c_0_100, negated_conjecture, (~l2_struct_0(esk2_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_80]), c_0_39]), c_0_40])]), c_0_75]), c_0_99]), c_0_55])).
cnf(c_0_101, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_61]), c_0_24])]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 102
# Proof object clause steps            : 73
# Proof object formula steps           : 29
# Proof object conjectures             : 52
# Proof object clause conjectures      : 49
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 31
# Proof object initial formulas used   : 11
# Proof object generating inferences   : 40
# Proof object simplifying inferences  : 164
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 11
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 36
# Removed in clause preprocessing      : 0
# Initial clauses in saturation        : 36
# Processed clauses                    : 263
# ...of these trivial                  : 0
# ...subsumed                          : 73
# ...remaining for further processing  : 190
# Other redundant clauses eliminated   : 2
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 21
# Backward-rewritten                   : 0
# Generated clauses                    : 489
# ...of the previous two non-trivial   : 410
# Contextual simplify-reflections      : 29
# Paramodulations                      : 484
# Factorizations                       : 2
# NegExts                              : 0
# Equation resolutions                 : 3
# 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  : 131
#    Positive orientable unit clauses  : 14
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 3
#    Non-unit-clauses                  : 114
# Current number of unprocessed clauses: 203
# ...number of literals in the above   : 1465
# Current number of archived formulas  : 0
# Current number of archived clauses   : 57
# Clause-clause subsumption calls (NU) : 9019
# Rec. Clause-clause subsumption calls : 1646
# Non-unit clause-clause subsumptions  : 123
# Unit Clause-clause subsumption calls : 49
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 0
# BW rewrite match successes           : 0
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 36198

# -------------------------------------------------
# User time                : 0.047 s
# System time              : 0.004 s
# Total time               : 0.050 s
# Maximum resident set size: 3468 pages
