# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S2SI
# and selection function SelectNewComplexAHP.
#
# Preprocessing time       : 0.022 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(dt_k2_binom, axiom, ![X1, X2, X3]:(((((~(v2_struct_0(X1))&v1_group_1(X1))&l3_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))&v7_ordinal1(X3))=>m1_subset_1(k2_binom(X1,X2,X3),u1_struct_0(X1))), file('field_16/field_16__t37_field_16', dt_k2_binom)).
fof(t37_field_16, conjecture, ![X1]:(((((((((((~(v2_struct_0(X1))&~(v6_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))&v1_group_1(X1))&v3_group_1(X1))&l6_algstr_0(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))&v1_field_4(X2,X1))&l6_algstr_0(X2))=>![X3]:((~(v1_zfmisc_1(X3))&v7_ordinal1(X3))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>(r1_field_4(X1,X2,k7_field_16(X1,X3),X4)<=>k2_binom(X2,X4,X3)=X4))))), file('field_16/field_16__t37_field_16', t37_field_16)).
fof(dt_l4_algstr_0, axiom, ![X1]:(l4_algstr_0(X1)=>(l3_struct_0(X1)&l3_algstr_0(X1))), file('field_16/field_16__t37_field_16', dt_l4_algstr_0)).
fof(dt_l5_algstr_0, axiom, ![X1]:(l5_algstr_0(X1)=>(l4_algstr_0(X1)&l4_struct_0(X1))), file('field_16/field_16__t37_field_16', dt_l5_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__t37_field_16', dt_l6_algstr_0)).
fof(d2_field_4, axiom, ![X1]:(((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>![X2]:((((((((((~(v2_struct_0(X2))&v13_algstr_0(X2))&v4_vectsp_1(X2))&v5_vectsp_1(X2))&v2_rlvect_1(X2))&v3_rlvect_1(X2))&v4_rlvect_1(X2))&v3_group_1(X2))&v1_field_4(X2,X1))&l6_algstr_0(X2))=>![X3]:(m1_ring_4(X3,X1,u1_struct_0(k12_polynom3(X1)))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>(r1_field_4(X1,X2,X3,X4)<=>k1_algnum_1(X1,X2,X3,X4)=k4_struct_0(X2)))))), file('field_16/field_16__t37_field_16', d2_field_4)).
fof(t36_field_16, axiom, ![X1]:((((((((((~(v2_struct_0(X1))&~(v6_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]:((((((((((~(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))&v1_field_4(X2,X1))&l6_algstr_0(X2))=>![X3]:((~(v1_zfmisc_1(X3))&v7_ordinal1(X3))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>k1_algnum_1(X1,X2,k7_field_16(X1,X3),X4)=k5_algstr_0(X2,k2_binom(X2,X4,X3),X4))))), file('field_16/field_16__t37_field_16', t36_field_16)).
fof(cc5_vectsp_1, axiom, ![X1]:(l4_algstr_0(X1)=>((~(v2_struct_0(X1))&v4_vectsp_1(X1))=>(~(v2_struct_0(X1))&v1_group_1(X1)))), file('field_16/field_16__t37_field_16', cc5_vectsp_1)).
fof(dt_k7_field_16, axiom, ![X1, X2]:((((((((((((~(v2_struct_0(X1))&~(v6_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_zfmisc_1(X2)))&v7_ordinal1(X2))=>(~(v3_ring_4(k7_field_16(X1,X2),X1))&m1_ring_4(k7_field_16(X1,X2),X1,u1_struct_0(k12_polynom3(X1))))), file('field_16/field_16__t37_field_16', dt_k7_field_16)).
fof(t21_rlvect_1, axiom, ![X1]:(((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&l2_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(k5_algstr_0(X1,X2,X3)=k4_struct_0(X1)=>X2=X3)))), file('field_16/field_16__t37_field_16', t21_rlvect_1)).
fof(t15_rlvect_1, axiom, ![X1]:(((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&l2_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k5_algstr_0(X1,X2,X2)=k4_struct_0(X1))), file('field_16/field_16__t37_field_16', t15_rlvect_1)).
fof(c_0_11, plain, ![X1, X2, X3]:(((((~v2_struct_0(X1)&v1_group_1(X1))&l3_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))&v7_ordinal1(X3))=>m1_subset_1(k2_binom(X1,X2,X3),u1_struct_0(X1))), inference(fof_simplification,[status(thm)],[dt_k2_binom])).
fof(c_0_12, negated_conjecture, ~(![X1]:(((((((((((~v2_struct_0(X1)&~v6_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))&v1_group_1(X1))&v3_group_1(X1))&l6_algstr_0(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))&v1_field_4(X2,X1))&l6_algstr_0(X2))=>![X3]:((~v1_zfmisc_1(X3)&v7_ordinal1(X3))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>(r1_field_4(X1,X2,k7_field_16(X1,X3),X4)<=>k2_binom(X2,X4,X3)=X4)))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t37_field_16])])).
fof(c_0_13, plain, ![X40, X41, X42]:(v2_struct_0(X40)|~v1_group_1(X40)|~l3_algstr_0(X40)|~m1_subset_1(X41,u1_struct_0(X40))|~v7_ordinal1(X42)|m1_subset_1(k2_binom(X40,X41,X42),u1_struct_0(X40))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])).
fof(c_0_14, negated_conjecture, (((((((((((~v2_struct_0(esk1_0)&~v6_struct_0(esk1_0))&v13_algstr_0(esk1_0))&v2_rlvect_1(esk1_0))&v3_rlvect_1(esk1_0))&v4_rlvect_1(esk1_0))&v4_vectsp_1(esk1_0))&v5_vectsp_1(esk1_0))&v1_group_1(esk1_0))&v3_group_1(esk1_0))&l6_algstr_0(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))&v1_field_4(esk2_0,esk1_0))&l6_algstr_0(esk2_0))&((~v1_zfmisc_1(esk3_0)&v7_ordinal1(esk3_0))&(m1_subset_1(esk4_0,u1_struct_0(esk2_0))&((~r1_field_4(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)|k2_binom(esk2_0,esk4_0,esk3_0)!=esk4_0)&(r1_field_4(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)|k2_binom(esk2_0,esk4_0,esk3_0)=esk4_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])).
cnf(c_0_15, plain, (v2_struct_0(X1)|m1_subset_1(k2_binom(X1,X2,X3),u1_struct_0(X1))|~v1_group_1(X1)|~l3_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))|~v7_ordinal1(X3)), inference(split_conjunct,[status(thm)],[c_0_13])).
cnf(c_0_16, negated_conjecture, (m1_subset_1(esk4_0,u1_struct_0(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_17, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
fof(c_0_18, plain, ![X45]:((l3_struct_0(X45)|~l4_algstr_0(X45))&(l3_algstr_0(X45)|~l4_algstr_0(X45))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l4_algstr_0])])])).
fof(c_0_19, plain, ![X46]:((l4_algstr_0(X46)|~l5_algstr_0(X46))&(l4_struct_0(X46)|~l5_algstr_0(X46))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_algstr_0])])])).
fof(c_0_20, plain, ![X47]:((l2_algstr_0(X47)|~l6_algstr_0(X47))&(l5_algstr_0(X47)|~l6_algstr_0(X47))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])).
fof(c_0_21, plain, ![X1]:(((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>![X2]:((((((((((~v2_struct_0(X2)&v13_algstr_0(X2))&v4_vectsp_1(X2))&v5_vectsp_1(X2))&v2_rlvect_1(X2))&v3_rlvect_1(X2))&v4_rlvect_1(X2))&v3_group_1(X2))&v1_field_4(X2,X1))&l6_algstr_0(X2))=>![X3]:(m1_ring_4(X3,X1,u1_struct_0(k12_polynom3(X1)))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>(r1_field_4(X1,X2,X3,X4)<=>k1_algnum_1(X1,X2,X3,X4)=k4_struct_0(X2)))))), inference(fof_simplification,[status(thm)],[d2_field_4])).
fof(c_0_22, plain, ![X1]:((((((((((~v2_struct_0(X1)&~v6_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]:((((((((((~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))&v1_field_4(X2,X1))&l6_algstr_0(X2))=>![X3]:((~v1_zfmisc_1(X3)&v7_ordinal1(X3))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>k1_algnum_1(X1,X2,k7_field_16(X1,X3),X4)=k5_algstr_0(X2,k2_binom(X2,X4,X3),X4))))), inference(fof_simplification,[status(thm)],[t36_field_16])).
cnf(c_0_23, negated_conjecture, (m1_subset_1(k2_binom(esk2_0,esk4_0,X1),u1_struct_0(esk2_0))|~l3_algstr_0(esk2_0)|~v7_ordinal1(X1)|~v1_group_1(esk2_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_17])).
cnf(c_0_24, plain, (l3_algstr_0(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_18])).
cnf(c_0_25, plain, (l4_algstr_0(X1)|~l5_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_26, plain, (l5_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_20])).
fof(c_0_27, plain, ![X1]:(l4_algstr_0(X1)=>((~v2_struct_0(X1)&v4_vectsp_1(X1))=>(~v2_struct_0(X1)&v1_group_1(X1)))), inference(fof_simplification,[status(thm)],[cc5_vectsp_1])).
fof(c_0_28, plain, ![X36, X37, X38, X39]:((~r1_field_4(X36,X37,X38,X39)|k1_algnum_1(X36,X37,X38,X39)=k4_struct_0(X37)|~m1_subset_1(X39,u1_struct_0(X37))|~m1_ring_4(X38,X36,u1_struct_0(k12_polynom3(X36)))|(v2_struct_0(X37)|~v13_algstr_0(X37)|~v4_vectsp_1(X37)|~v5_vectsp_1(X37)|~v2_rlvect_1(X37)|~v3_rlvect_1(X37)|~v4_rlvect_1(X37)|~v3_group_1(X37)|~v1_field_4(X37,X36)|~l6_algstr_0(X37))|(v2_struct_0(X36)|~v13_algstr_0(X36)|~v4_vectsp_1(X36)|~v5_vectsp_1(X36)|~v2_rlvect_1(X36)|~v3_rlvect_1(X36)|~v4_rlvect_1(X36)|~v3_group_1(X36)|~l6_algstr_0(X36)))&(k1_algnum_1(X36,X37,X38,X39)!=k4_struct_0(X37)|r1_field_4(X36,X37,X38,X39)|~m1_subset_1(X39,u1_struct_0(X37))|~m1_ring_4(X38,X36,u1_struct_0(k12_polynom3(X36)))|(v2_struct_0(X37)|~v13_algstr_0(X37)|~v4_vectsp_1(X37)|~v5_vectsp_1(X37)|~v2_rlvect_1(X37)|~v3_rlvect_1(X37)|~v4_rlvect_1(X37)|~v3_group_1(X37)|~v1_field_4(X37,X36)|~l6_algstr_0(X37))|(v2_struct_0(X36)|~v13_algstr_0(X36)|~v4_vectsp_1(X36)|~v5_vectsp_1(X36)|~v2_rlvect_1(X36)|~v3_rlvect_1(X36)|~v4_rlvect_1(X36)|~v3_group_1(X36)|~l6_algstr_0(X36)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])).
fof(c_0_29, plain, ![X53, X54, X55, X56]:(v2_struct_0(X53)|v6_struct_0(X53)|~v13_algstr_0(X53)|~v2_rlvect_1(X53)|~v3_rlvect_1(X53)|~v4_rlvect_1(X53)|~v4_vectsp_1(X53)|~v5_vectsp_1(X53)|~v3_group_1(X53)|~l6_algstr_0(X53)|(v2_struct_0(X54)|~v13_algstr_0(X54)|~v2_rlvect_1(X54)|~v3_rlvect_1(X54)|~v4_rlvect_1(X54)|~v4_vectsp_1(X54)|~v5_vectsp_1(X54)|~v3_group_1(X54)|~v1_field_4(X54,X53)|~l6_algstr_0(X54)|(v1_zfmisc_1(X55)|~v7_ordinal1(X55)|(~m1_subset_1(X56,u1_struct_0(X54))|k1_algnum_1(X53,X54,k7_field_16(X53,X55),X56)=k5_algstr_0(X54,k2_binom(X54,X56,X55),X56))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])).
cnf(c_0_30, negated_conjecture, (m1_subset_1(k2_binom(esk2_0,esk4_0,X1),u1_struct_0(esk2_0))|~l4_algstr_0(esk2_0)|~v7_ordinal1(X1)|~v1_group_1(esk2_0)), inference(spm,[status(thm)],[c_0_23, c_0_24])).
cnf(c_0_31, plain, (l4_algstr_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_25, c_0_26])).
cnf(c_0_32, negated_conjecture, (l6_algstr_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
fof(c_0_33, plain, ![X35]:((~v2_struct_0(X35)|(v2_struct_0(X35)|~v4_vectsp_1(X35))|~l4_algstr_0(X35))&(v1_group_1(X35)|(v2_struct_0(X35)|~v4_vectsp_1(X35))|~l4_algstr_0(X35))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])).
cnf(c_0_34, plain, (k1_algnum_1(X1,X2,X3,X4)=k4_struct_0(X2)|v2_struct_0(X2)|v2_struct_0(X1)|~r1_field_4(X1,X2,X3,X4)|~m1_subset_1(X4,u1_struct_0(X2))|~m1_ring_4(X3,X1,u1_struct_0(k12_polynom3(X1)))|~v13_algstr_0(X2)|~v4_vectsp_1(X2)|~v5_vectsp_1(X2)|~v2_rlvect_1(X2)|~v3_rlvect_1(X2)|~v4_rlvect_1(X2)|~v3_group_1(X2)|~v1_field_4(X2,X1)|~l6_algstr_0(X2)|~v13_algstr_0(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_35, negated_conjecture, (v3_group_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_36, negated_conjecture, (v5_vectsp_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_37, negated_conjecture, (v4_vectsp_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_38, negated_conjecture, (v4_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_39, negated_conjecture, (v3_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_40, negated_conjecture, (v2_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_41, negated_conjecture, (v13_algstr_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_42, plain, (v2_struct_0(X1)|v6_struct_0(X1)|v2_struct_0(X2)|v1_zfmisc_1(X3)|k1_algnum_1(X1,X2,k7_field_16(X1,X3),X4)=k5_algstr_0(X2,k2_binom(X2,X4,X3),X4)|~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)|~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)|~v1_field_4(X2,X1)|~l6_algstr_0(X2)|~v7_ordinal1(X3)|~m1_subset_1(X4,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_43, negated_conjecture, (m1_subset_1(k2_binom(esk2_0,esk4_0,X1),u1_struct_0(esk2_0))|~v7_ordinal1(X1)|~v1_group_1(esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32])])).
cnf(c_0_44, plain, (v1_group_1(X1)|v2_struct_0(X1)|~v4_vectsp_1(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_33])).
cnf(c_0_45, negated_conjecture, (k1_algnum_1(X1,esk2_0,X2,esk4_0)=k4_struct_0(esk2_0)|v2_struct_0(X1)|~m1_ring_4(X2,X1,u1_struct_0(k12_polynom3(X1)))|~r1_field_4(X1,esk2_0,X2,esk4_0)|~v1_field_4(esk2_0,X1)|~l6_algstr_0(X1)|~v3_group_1(X1)|~v5_vectsp_1(X1)|~v4_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v2_rlvect_1(X1)|~v13_algstr_0(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_34, c_0_16]), c_0_32]), c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_40]), c_0_41])]), c_0_17])).
cnf(c_0_46, negated_conjecture, (v1_field_4(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_47, negated_conjecture, (l6_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_48, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_49, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_50, negated_conjecture, (v4_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_51, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_52, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_53, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_54, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_55, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
fof(c_0_56, plain, ![X1, X2]:((((((((((((~v2_struct_0(X1)&~v6_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_zfmisc_1(X2))&v7_ordinal1(X2))=>(~v3_ring_4(k7_field_16(X1,X2),X1)&m1_ring_4(k7_field_16(X1,X2),X1,u1_struct_0(k12_polynom3(X1))))), inference(fof_simplification,[status(thm)],[dt_k7_field_16])).
fof(c_0_57, plain, ![X1]:(((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&l2_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(k5_algstr_0(X1,X2,X3)=k4_struct_0(X1)=>X2=X3)))), inference(fof_simplification,[status(thm)],[t21_rlvect_1])).
cnf(c_0_58, negated_conjecture, (k1_algnum_1(X1,esk2_0,k7_field_16(X1,X2),esk4_0)=k5_algstr_0(esk2_0,k2_binom(esk2_0,esk4_0,X2),esk4_0)|v1_zfmisc_1(X2)|v6_struct_0(X1)|v2_struct_0(X1)|~v7_ordinal1(X2)|~v1_field_4(esk2_0,X1)|~l6_algstr_0(X1)|~v3_group_1(X1)|~v5_vectsp_1(X1)|~v4_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v2_rlvect_1(X1)|~v13_algstr_0(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_42, c_0_16]), c_0_32]), c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_40]), c_0_41])]), c_0_17])).
cnf(c_0_59, negated_conjecture, (~v6_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_60, negated_conjecture, (m1_subset_1(k2_binom(esk2_0,esk4_0,X1),u1_struct_0(esk2_0))|~l4_algstr_0(esk2_0)|~v7_ordinal1(X1)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_37])]), c_0_17])).
cnf(c_0_61, negated_conjecture, (k1_algnum_1(esk1_0,esk2_0,X1,esk4_0)=k4_struct_0(esk2_0)|~m1_ring_4(X1,esk1_0,u1_struct_0(k12_polynom3(esk1_0)))|~r1_field_4(esk1_0,esk2_0,X1,esk4_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(spm,[status(thm)],[c_0_45, c_0_46]), c_0_47]), c_0_48]), c_0_49]), c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54])]), c_0_55])).
cnf(c_0_62, negated_conjecture, (r1_field_4(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)|k2_binom(esk2_0,esk4_0,esk3_0)=esk4_0), inference(split_conjunct,[status(thm)],[c_0_14])).
fof(c_0_63, plain, ![X43, X44]:((~v3_ring_4(k7_field_16(X43,X44),X43)|(v2_struct_0(X43)|v6_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_zfmisc_1(X44)|~v7_ordinal1(X44)))&(m1_ring_4(k7_field_16(X43,X44),X43,u1_struct_0(k12_polynom3(X43)))|(v2_struct_0(X43)|v6_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_zfmisc_1(X44)|~v7_ordinal1(X44)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])).
fof(c_0_64, plain, ![X1]:(((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&l2_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k5_algstr_0(X1,X2,X2)=k4_struct_0(X1))), inference(fof_simplification,[status(thm)],[t15_rlvect_1])).
fof(c_0_65, plain, ![X50, X51, X52]:(v2_struct_0(X50)|~v13_algstr_0(X50)|~v3_rlvect_1(X50)|~v4_rlvect_1(X50)|~l2_algstr_0(X50)|(~m1_subset_1(X51,u1_struct_0(X50))|(~m1_subset_1(X52,u1_struct_0(X50))|(k5_algstr_0(X50,X51,X52)!=k4_struct_0(X50)|X51=X52)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])).
cnf(c_0_66, negated_conjecture, (~v1_zfmisc_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_67, negated_conjecture, (k5_algstr_0(esk2_0,k2_binom(esk2_0,esk4_0,X1),esk4_0)=k1_algnum_1(esk1_0,esk2_0,k7_field_16(esk1_0,X1),esk4_0)|v1_zfmisc_1(X1)|~v7_ordinal1(X1)), inference(sr,[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(spm,[status(thm)],[c_0_58, c_0_46]), c_0_47]), c_0_48]), c_0_49]), c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54])]), c_0_59]), c_0_55])).
cnf(c_0_68, negated_conjecture, (v7_ordinal1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_69, negated_conjecture, (m1_subset_1(k2_binom(esk2_0,esk4_0,X1),u1_struct_0(esk2_0))|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_31]), c_0_32])])).
cnf(c_0_70, negated_conjecture, (k1_algnum_1(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)=k4_struct_0(esk2_0)|k2_binom(esk2_0,esk4_0,esk3_0)=esk4_0|~m1_ring_4(k7_field_16(esk1_0,esk3_0),esk1_0,u1_struct_0(k12_polynom3(esk1_0)))), inference(spm,[status(thm)],[c_0_61, c_0_62])).
cnf(c_0_71, plain, (m1_ring_4(k7_field_16(X1,X2),X1,u1_struct_0(k12_polynom3(X1)))|v2_struct_0(X1)|v6_struct_0(X1)|v1_zfmisc_1(X2)|~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)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_63])).
fof(c_0_72, plain, ![X48, X49]:(v2_struct_0(X48)|~v13_algstr_0(X48)|~v3_rlvect_1(X48)|~v4_rlvect_1(X48)|~l2_algstr_0(X48)|(~m1_subset_1(X49,u1_struct_0(X48))|k5_algstr_0(X48,X49,X49)=k4_struct_0(X48))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])).
cnf(c_0_73, plain, (v2_struct_0(X1)|X2=X3|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~l2_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))|~m1_subset_1(X3,u1_struct_0(X1))|k5_algstr_0(X1,X2,X3)!=k4_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_65])).
cnf(c_0_74, negated_conjecture, (k5_algstr_0(esk2_0,k2_binom(esk2_0,esk4_0,esk3_0),esk4_0)=k1_algnum_1(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_68])])).
cnf(c_0_75, negated_conjecture, (m1_subset_1(k2_binom(esk2_0,esk4_0,esk3_0),u1_struct_0(esk2_0))), inference(spm,[status(thm)],[c_0_69, c_0_68])).
cnf(c_0_76, negated_conjecture, (k1_algnum_1(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)=k4_struct_0(esk2_0)|k2_binom(esk2_0,esk4_0,esk3_0)=esk4_0), inference(sr,[status(thm)],[inference(sr,[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(spm,[status(thm)],[c_0_70, c_0_71]), c_0_68]), c_0_47]), c_0_48]), c_0_49]), c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54])]), c_0_66]), c_0_59]), c_0_55])).
cnf(c_0_77, plain, (v2_struct_0(X1)|k5_algstr_0(X1,X2,X2)=k4_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~l2_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_72])).
cnf(c_0_78, plain, (r1_field_4(X1,X2,X3,X4)|v2_struct_0(X2)|v2_struct_0(X1)|k1_algnum_1(X1,X2,X3,X4)!=k4_struct_0(X2)|~m1_subset_1(X4,u1_struct_0(X2))|~m1_ring_4(X3,X1,u1_struct_0(k12_polynom3(X1)))|~v13_algstr_0(X2)|~v4_vectsp_1(X2)|~v5_vectsp_1(X2)|~v2_rlvect_1(X2)|~v3_rlvect_1(X2)|~v4_rlvect_1(X2)|~v3_group_1(X2)|~v1_field_4(X2,X1)|~l6_algstr_0(X2)|~v13_algstr_0(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_79, negated_conjecture, (k2_binom(esk2_0,esk4_0,esk3_0)=esk4_0|~l2_algstr_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(spm,[status(thm)],[c_0_73, c_0_74]), c_0_16]), c_0_75]), c_0_38]), c_0_39]), c_0_41])]), c_0_17]), c_0_76])).
cnf(c_0_80, plain, (l2_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_81, negated_conjecture, (k5_algstr_0(esk2_0,esk4_0,esk4_0)=k4_struct_0(esk2_0)|~l2_algstr_0(esk2_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_16]), c_0_38]), c_0_39]), c_0_41])]), c_0_17])).
cnf(c_0_82, negated_conjecture, (r1_field_4(X1,esk2_0,X2,esk4_0)|v2_struct_0(X1)|k1_algnum_1(X1,esk2_0,X2,esk4_0)!=k4_struct_0(esk2_0)|~m1_ring_4(X2,X1,u1_struct_0(k12_polynom3(X1)))|~v1_field_4(esk2_0,X1)|~l6_algstr_0(X1)|~v3_group_1(X1)|~v5_vectsp_1(X1)|~v4_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v2_rlvect_1(X1)|~v13_algstr_0(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_78, c_0_16]), c_0_32]), c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_40]), c_0_41])]), c_0_17])).
cnf(c_0_83, negated_conjecture, (k2_binom(esk2_0,esk4_0,esk3_0)=esk4_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80]), c_0_32])])).
cnf(c_0_84, negated_conjecture, (k5_algstr_0(esk2_0,esk4_0,esk4_0)=k4_struct_0(esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_80]), c_0_32])])).
cnf(c_0_85, negated_conjecture, (~r1_field_4(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)|k2_binom(esk2_0,esk4_0,esk3_0)!=esk4_0), inference(split_conjunct,[status(thm)],[c_0_14])).
cnf(c_0_86, negated_conjecture, (r1_field_4(esk1_0,esk2_0,X1,esk4_0)|k1_algnum_1(esk1_0,esk2_0,X1,esk4_0)!=k4_struct_0(esk2_0)|~m1_ring_4(X1,esk1_0,u1_struct_0(k12_polynom3(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(spm,[status(thm)],[c_0_82, c_0_46]), c_0_47]), c_0_48]), c_0_49]), c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54])]), c_0_55])).
cnf(c_0_87, negated_conjecture, (k1_algnum_1(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)=k4_struct_0(esk2_0)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_83]), c_0_84])).
cnf(c_0_88, negated_conjecture, (~r1_field_4(esk1_0,esk2_0,k7_field_16(esk1_0,esk3_0),esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85, c_0_83])])).
cnf(c_0_89, negated_conjecture, (~m1_ring_4(k7_field_16(esk1_0,esk3_0),esk1_0,u1_struct_0(k12_polynom3(esk1_0)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_88])).
cnf(c_0_90, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[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(spm,[status(thm)],[c_0_89, c_0_71]), c_0_68]), c_0_47]), c_0_48]), c_0_49]), c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54])]), c_0_66]), c_0_59]), c_0_55]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 91
# Proof object clause steps            : 61
# Proof object formula steps           : 30
# Proof object conjectures             : 51
# Proof object clause conjectures      : 48
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 37
# Proof object initial formulas used   : 11
# Proof object generating inferences   : 22
# Proof object simplifying inferences  : 119
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 11
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 42
# Removed in clause preprocessing      : 1
# Initial clauses in saturation        : 41
# Processed clauses                    : 125
# ...of these trivial                  : 0
# ...subsumed                          : 3
# ...remaining for further processing  : 122
# Other redundant clauses eliminated   : 0
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 13
# Backward-rewritten                   : 16
# Generated clauses                    : 52
# ...of the previous two non-trivial   : 57
# Contextual simplify-reflections      : 1
# Paramodulations                      : 52
# 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  : 52
#    Positive orientable unit clauses  : 23
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 6
#    Non-unit-clauses                  : 23
# Current number of unprocessed clauses: 14
# ...number of literals in the above   : 134
# Current number of archived formulas  : 0
# Current number of archived clauses   : 70
# Clause-clause subsumption calls (NU) : 2206
# Rec. Clause-clause subsumption calls : 143
# Non-unit clause-clause subsumptions  : 17
# Unit Clause-clause subsumption calls : 7
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 15
# BW rewrite match successes           : 3
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 7697

# -------------------------------------------------
# User time                : 0.026 s
# System time              : 0.004 s
# Total time               : 0.030 s
# Maximum resident set size: 3404 pages
