# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___302_C18_F1_URBAN_RG_S04BN
# and selection function PSelectComplexExceptUniqMaxHorn.
#
# Preprocessing time       : 0.030 s

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
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__l55_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__l55_field_16', dt_k7_field_16)).
fof(l55_field_16, conjecture, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~(v8_ordinal1(X2)))=>![X3]:(((((((((((((~(v2_struct_0(X3))&~(v6_struct_0(X3)))&v13_algstr_0(X3))&v33_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))&v5_group_1(X3))&v3_ring_3(X3,X1))&l6_algstr_0(X3))=>![X4]:(((((((((((((~(v2_struct_0(X4))&~(v6_struct_0(X4)))&v13_algstr_0(X4))&v33_algstr_0(X4))&v2_rlvect_1(X4))&v3_rlvect_1(X4))&v4_rlvect_1(X4))&v4_vectsp_1(X4))&v5_vectsp_1(X4))&v3_group_1(X4))&v5_group_1(X4))&v1_field_4(X4,X3))&l6_algstr_0(X4))=>(k7_struct_0(X4)=k1_newton(X1,X2)=>![X5]:(m1_subset_1(X5,u1_struct_0(X4))=>k1_algnum_1(X3,X4,k7_field_16(X3,k1_newton(X1,X2)),X5)=k4_struct_0(X4))))))), file('field_16/field_16__l55_field_16', l55_field_16)).
fof(dt_l5_algstr_0, axiom, ![X1]:(l5_algstr_0(X1)=>(l4_algstr_0(X1)&l4_struct_0(X1))), file('field_16/field_16__l55_field_16', dt_l5_algstr_0)).
fof(t28_field_16, axiom, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~(v8_ordinal1(X2)))=>![X3]:((((((((((((~(v2_struct_0(X3))&~(v6_struct_0(X3)))&v13_algstr_0(X3))&v33_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))&v5_group_1(X3))&l6_algstr_0(X3))=>(k7_struct_0(X3)=k1_newton(X1,X2)=>![X4]:(m1_subset_1(X4,u1_struct_0(X3))=>k2_binom(X3,X4,k1_newton(X1,X2))=X4))))), file('field_16/field_16__l55_field_16', t28_field_16)).
fof(t37_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))&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__l55_field_16', t37_field_16)).
fof(dt_l6_algstr_0, axiom, ![X1]:(l6_algstr_0(X1)=>(l2_algstr_0(X1)&l5_algstr_0(X1))), file('field_16/field_16__l55_field_16', dt_l6_algstr_0)).
fof(fc4_newton, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>v7_ordinal1(k1_newton(X1,X2))), file('field_16/field_16__l55_field_16', fc4_newton)).
fof(fc13_field_16, axiom, ![X1, X2]:(((v7_ordinal1(X1)&v7_ordinal1(X2))&~(v8_ordinal1(X2)))=>v2_field_16(k1_newton(X1,X2),X1)), file('field_16/field_16__l55_field_16', fc13_field_16)).
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__l55_field_16', d2_field_4)).
fof(cc3_field_16, axiom, ![X1]:((~(v1_zfmisc_1(X1))&v7_ordinal1(X1))=>![X2]:((v7_ordinal1(X2)&v2_field_16(X2,X1))=>((~(v1_zfmisc_1(X2))&v7_ordinal1(X2))&v2_field_16(X2,X1)))), file('field_16/field_16__l55_field_16', cc3_field_16)).
fof(cc1_nat_6, axiom, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>(~(v1_zfmisc_1(X1))&v7_ordinal1(X1))), file('field_16/field_16__l55_field_16', cc1_nat_6)).
fof(c_0_12, 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_13, 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_14, negated_conjecture, ~(![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~v8_ordinal1(X2))=>![X3]:(((((((((((((~v2_struct_0(X3)&~v6_struct_0(X3))&v13_algstr_0(X3))&v33_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))&v5_group_1(X3))&v3_ring_3(X3,X1))&l6_algstr_0(X3))=>![X4]:(((((((((((((~v2_struct_0(X4)&~v6_struct_0(X4))&v13_algstr_0(X4))&v33_algstr_0(X4))&v2_rlvect_1(X4))&v3_rlvect_1(X4))&v4_rlvect_1(X4))&v4_vectsp_1(X4))&v5_vectsp_1(X4))&v3_group_1(X4))&v5_group_1(X4))&v1_field_4(X4,X3))&l6_algstr_0(X4))=>(k7_struct_0(X4)=k1_newton(X1,X2)=>![X5]:(m1_subset_1(X5,u1_struct_0(X4))=>k1_algnum_1(X3,X4,k7_field_16(X3,k1_newton(X1,X2)),X5)=k4_struct_0(X4)))))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l55_field_16])])).
fof(c_0_15, plain, ![X43]:((~v2_struct_0(X43)|(v2_struct_0(X43)|~v4_vectsp_1(X43))|~l4_algstr_0(X43))&(v1_group_1(X43)|(v2_struct_0(X43)|~v4_vectsp_1(X43))|~l4_algstr_0(X43))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])).
fof(c_0_16, plain, ![X50]:((l4_algstr_0(X50)|~l5_algstr_0(X50))&(l4_struct_0(X50)|~l5_algstr_0(X50))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_algstr_0])])])).
fof(c_0_17, plain, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~v8_ordinal1(X2))=>![X3]:((((((((((((~v2_struct_0(X3)&~v6_struct_0(X3))&v13_algstr_0(X3))&v33_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))&v5_group_1(X3))&l6_algstr_0(X3))=>(k7_struct_0(X3)=k1_newton(X1,X2)=>![X4]:(m1_subset_1(X4,u1_struct_0(X3))=>k2_binom(X3,X4,k1_newton(X1,X2))=X4))))), inference(fof_simplification,[status(thm)],[t28_field_16])).
fof(c_0_18, plain, ![X48, X49]:((~v3_ring_4(k7_field_16(X48,X49),X48)|(v2_struct_0(X48)|v6_struct_0(X48)|~v13_algstr_0(X48)|~v2_rlvect_1(X48)|~v3_rlvect_1(X48)|~v4_rlvect_1(X48)|~v4_vectsp_1(X48)|~v5_vectsp_1(X48)|~v3_group_1(X48)|~l6_algstr_0(X48)|v1_zfmisc_1(X49)|~v7_ordinal1(X49)))&(m1_ring_4(k7_field_16(X48,X49),X48,u1_struct_0(k12_polynom3(X48)))|(v2_struct_0(X48)|v6_struct_0(X48)|~v13_algstr_0(X48)|~v2_rlvect_1(X48)|~v3_rlvect_1(X48)|~v4_rlvect_1(X48)|~v4_vectsp_1(X48)|~v5_vectsp_1(X48)|~v3_group_1(X48)|~l6_algstr_0(X48)|v1_zfmisc_1(X49)|~v7_ordinal1(X49)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])).
fof(c_0_19, negated_conjecture, ((v7_ordinal1(esk1_0)&v1_int_2(esk1_0))&((v7_ordinal1(esk2_0)&~v8_ordinal1(esk2_0))&(((((((((((((~v2_struct_0(esk3_0)&~v6_struct_0(esk3_0))&v13_algstr_0(esk3_0))&v33_algstr_0(esk3_0))&v2_rlvect_1(esk3_0))&v3_rlvect_1(esk3_0))&v4_rlvect_1(esk3_0))&v4_vectsp_1(esk3_0))&v5_vectsp_1(esk3_0))&v3_group_1(esk3_0))&v5_group_1(esk3_0))&v3_ring_3(esk3_0,esk1_0))&l6_algstr_0(esk3_0))&(((((((((((((~v2_struct_0(esk4_0)&~v6_struct_0(esk4_0))&v13_algstr_0(esk4_0))&v33_algstr_0(esk4_0))&v2_rlvect_1(esk4_0))&v3_rlvect_1(esk4_0))&v4_rlvect_1(esk4_0))&v4_vectsp_1(esk4_0))&v5_vectsp_1(esk4_0))&v3_group_1(esk4_0))&v5_group_1(esk4_0))&v1_field_4(esk4_0,esk3_0))&l6_algstr_0(esk4_0))&(k7_struct_0(esk4_0)=k1_newton(esk1_0,esk2_0)&(m1_subset_1(esk5_0,u1_struct_0(esk4_0))&k1_algnum_1(esk3_0,esk4_0,k7_field_16(esk3_0,k1_newton(esk1_0,esk2_0)),esk5_0)!=k4_struct_0(esk4_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])).
fof(c_0_20, 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))&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)],[t37_field_16])).
cnf(c_0_21, plain, (v1_group_1(X1)|v2_struct_0(X1)|~v4_vectsp_1(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_15])).
cnf(c_0_22, plain, (l4_algstr_0(X1)|~l5_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_16])).
fof(c_0_23, plain, ![X51]:((l2_algstr_0(X51)|~l6_algstr_0(X51))&(l5_algstr_0(X51)|~l6_algstr_0(X51))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])).
fof(c_0_24, plain, ![X56, X57, X58, X59]:(~v7_ordinal1(X56)|~v1_int_2(X56)|(~v7_ordinal1(X57)|v8_ordinal1(X57)|(v2_struct_0(X58)|v6_struct_0(X58)|~v13_algstr_0(X58)|~v33_algstr_0(X58)|~v2_rlvect_1(X58)|~v3_rlvect_1(X58)|~v4_rlvect_1(X58)|~v4_vectsp_1(X58)|~v5_vectsp_1(X58)|~v3_group_1(X58)|~v5_group_1(X58)|~l6_algstr_0(X58)|(k7_struct_0(X58)!=k1_newton(X56,X57)|(~m1_subset_1(X59,u1_struct_0(X58))|k2_binom(X58,X59,k1_newton(X56,X57))=X59))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])).
cnf(c_0_25, 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_18])).
cnf(c_0_26, negated_conjecture, (l6_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_27, negated_conjecture, (v3_group_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_28, negated_conjecture, (v5_vectsp_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_29, negated_conjecture, (v4_vectsp_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_30, negated_conjecture, (v4_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_31, negated_conjecture, (v3_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_32, negated_conjecture, (v2_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_33, negated_conjecture, (v13_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_34, negated_conjecture, (~v6_struct_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_35, negated_conjecture, (~v2_struct_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_36, plain, ![X54, X55]:(~v7_ordinal1(X54)|~v7_ordinal1(X55)|v7_ordinal1(k1_newton(X54,X55))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_newton])])).
fof(c_0_37, plain, ![X60, X61, X62, X63]:((~r1_field_4(X60,X61,k7_field_16(X60,X62),X63)|k2_binom(X61,X63,X62)=X63|~m1_subset_1(X63,u1_struct_0(X61))|(v1_zfmisc_1(X62)|~v7_ordinal1(X62))|(v2_struct_0(X61)|~v13_algstr_0(X61)|~v2_rlvect_1(X61)|~v3_rlvect_1(X61)|~v4_rlvect_1(X61)|~v4_vectsp_1(X61)|~v5_vectsp_1(X61)|~v3_group_1(X61)|~v1_field_4(X61,X60)|~l6_algstr_0(X61))|(v2_struct_0(X60)|v6_struct_0(X60)|~v13_algstr_0(X60)|~v2_rlvect_1(X60)|~v3_rlvect_1(X60)|~v4_rlvect_1(X60)|~v4_vectsp_1(X60)|~v5_vectsp_1(X60)|~v1_group_1(X60)|~v3_group_1(X60)|~l6_algstr_0(X60)))&(k2_binom(X61,X63,X62)!=X63|r1_field_4(X60,X61,k7_field_16(X60,X62),X63)|~m1_subset_1(X63,u1_struct_0(X61))|(v1_zfmisc_1(X62)|~v7_ordinal1(X62))|(v2_struct_0(X61)|~v13_algstr_0(X61)|~v2_rlvect_1(X61)|~v3_rlvect_1(X61)|~v4_rlvect_1(X61)|~v4_vectsp_1(X61)|~v5_vectsp_1(X61)|~v3_group_1(X61)|~v1_field_4(X61,X60)|~l6_algstr_0(X61))|(v2_struct_0(X60)|v6_struct_0(X60)|~v13_algstr_0(X60)|~v2_rlvect_1(X60)|~v3_rlvect_1(X60)|~v4_rlvect_1(X60)|~v4_vectsp_1(X60)|~v5_vectsp_1(X60)|~v1_group_1(X60)|~v3_group_1(X60)|~l6_algstr_0(X60)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])).
cnf(c_0_38, plain, (v1_group_1(X1)|v2_struct_0(X1)|~l5_algstr_0(X1)|~v4_vectsp_1(X1)), inference(spm,[status(thm)],[c_0_21, c_0_22])).
cnf(c_0_39, plain, (l5_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_23])).
cnf(c_0_40, plain, (v8_ordinal1(X2)|v2_struct_0(X3)|v6_struct_0(X3)|k2_binom(X3,X4,k1_newton(X1,X2))=X4|~v7_ordinal1(X1)|~v1_int_2(X1)|~v7_ordinal1(X2)|~v13_algstr_0(X3)|~v33_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)|~v5_group_1(X3)|~l6_algstr_0(X3)|k7_struct_0(X3)!=k1_newton(X1,X2)|~m1_subset_1(X4,u1_struct_0(X3))), inference(split_conjunct,[status(thm)],[c_0_24])).
cnf(c_0_41, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk4_0))), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_42, negated_conjecture, (k7_struct_0(esk4_0)=k1_newton(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_43, negated_conjecture, (l6_algstr_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_44, negated_conjecture, (v5_group_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_45, negated_conjecture, (v3_group_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_46, negated_conjecture, (v5_vectsp_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_47, negated_conjecture, (v4_vectsp_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_48, negated_conjecture, (v4_rlvect_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_49, negated_conjecture, (v3_rlvect_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_50, negated_conjecture, (v2_rlvect_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_51, negated_conjecture, (v33_algstr_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_52, negated_conjecture, (v13_algstr_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_53, negated_conjecture, (~v6_struct_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_54, negated_conjecture, (~v2_struct_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_55, negated_conjecture, (m1_ring_4(k7_field_16(esk3_0,X1),esk3_0,u1_struct_0(k12_polynom3(esk3_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(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33])]), c_0_34]), c_0_35])).
cnf(c_0_56, plain, (v7_ordinal1(k1_newton(X1,X2))|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_36])).
cnf(c_0_57, plain, (r1_field_4(X4,X1,k7_field_16(X4,X3),X2)|v1_zfmisc_1(X3)|v2_struct_0(X1)|v2_struct_0(X4)|v6_struct_0(X4)|k2_binom(X1,X2,X3)!=X2|~m1_subset_1(X2,u1_struct_0(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)|~v1_field_4(X1,X4)|~l6_algstr_0(X1)|~v13_algstr_0(X4)|~v2_rlvect_1(X4)|~v3_rlvect_1(X4)|~v4_rlvect_1(X4)|~v4_vectsp_1(X4)|~v5_vectsp_1(X4)|~v1_group_1(X4)|~v3_group_1(X4)|~l6_algstr_0(X4)), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_58, plain, (v1_group_1(X1)|v2_struct_0(X1)|~l6_algstr_0(X1)|~v4_vectsp_1(X1)), inference(spm,[status(thm)],[c_0_38, c_0_39])).
cnf(c_0_59, negated_conjecture, (k2_binom(esk4_0,esk5_0,k1_newton(X1,X2))=esk5_0|v8_ordinal1(X2)|k1_newton(esk1_0,esk2_0)!=k1_newton(X1,X2)|~v1_int_2(X1)|~v7_ordinal1(X2)|~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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42]), c_0_43]), c_0_44]), 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])).
cnf(c_0_60, negated_conjecture, (v1_int_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_61, negated_conjecture, (v7_ordinal1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_62, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_63, negated_conjecture, (~v8_ordinal1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_64, plain, ![X1, X2]:(((v7_ordinal1(X1)&v7_ordinal1(X2))&~v8_ordinal1(X2))=>v2_field_16(k1_newton(X1,X2),X1)), inference(fof_simplification,[status(thm)],[fc13_field_16])).
fof(c_0_65, 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])).
cnf(c_0_66, negated_conjecture, (m1_ring_4(k7_field_16(esk3_0,k1_newton(X1,X2)),esk3_0,u1_struct_0(k12_polynom3(esk3_0)))|v1_zfmisc_1(k1_newton(X1,X2))|~v7_ordinal1(X2)|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_55, c_0_56])).
cnf(c_0_67, negated_conjecture, (r1_field_4(X1,esk4_0,k7_field_16(X1,X2),esk5_0)|v1_zfmisc_1(X2)|v6_struct_0(X1)|v2_struct_0(X1)|k2_binom(esk4_0,esk5_0,X2)!=esk5_0|~v1_field_4(esk4_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)|~v7_ordinal1(X2)), 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(spm,[status(thm)],[c_0_57, c_0_41]), c_0_43]), c_0_45]), c_0_46]), c_0_47]), c_0_48]), c_0_49]), c_0_50]), c_0_52])]), c_0_54]), c_0_58])).
cnf(c_0_68, negated_conjecture, (k2_binom(esk4_0,esk5_0,k1_newton(esk1_0,esk2_0))=esk5_0), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_59]), c_0_60]), c_0_61]), c_0_62])]), c_0_63])).
fof(c_0_69, plain, ![X1]:((~v1_zfmisc_1(X1)&v7_ordinal1(X1))=>![X2]:((v7_ordinal1(X2)&v2_field_16(X2,X1))=>((~v1_zfmisc_1(X2)&v7_ordinal1(X2))&v2_field_16(X2,X1)))), inference(fof_simplification,[status(thm)],[cc3_field_16])).
fof(c_0_70, plain, ![X52, X53]:(~v7_ordinal1(X52)|~v7_ordinal1(X53)|v8_ordinal1(X53)|v2_field_16(k1_newton(X52,X53),X52)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])).
fof(c_0_71, plain, ![X44, X45, X46, X47]:((~r1_field_4(X44,X45,X46,X47)|k1_algnum_1(X44,X45,X46,X47)=k4_struct_0(X45)|~m1_subset_1(X47,u1_struct_0(X45))|~m1_ring_4(X46,X44,u1_struct_0(k12_polynom3(X44)))|(v2_struct_0(X45)|~v13_algstr_0(X45)|~v4_vectsp_1(X45)|~v5_vectsp_1(X45)|~v2_rlvect_1(X45)|~v3_rlvect_1(X45)|~v4_rlvect_1(X45)|~v3_group_1(X45)|~v1_field_4(X45,X44)|~l6_algstr_0(X45))|(v2_struct_0(X44)|~v13_algstr_0(X44)|~v4_vectsp_1(X44)|~v5_vectsp_1(X44)|~v2_rlvect_1(X44)|~v3_rlvect_1(X44)|~v4_rlvect_1(X44)|~v3_group_1(X44)|~l6_algstr_0(X44)))&(k1_algnum_1(X44,X45,X46,X47)!=k4_struct_0(X45)|r1_field_4(X44,X45,X46,X47)|~m1_subset_1(X47,u1_struct_0(X45))|~m1_ring_4(X46,X44,u1_struct_0(k12_polynom3(X44)))|(v2_struct_0(X45)|~v13_algstr_0(X45)|~v4_vectsp_1(X45)|~v5_vectsp_1(X45)|~v2_rlvect_1(X45)|~v3_rlvect_1(X45)|~v4_rlvect_1(X45)|~v3_group_1(X45)|~v1_field_4(X45,X44)|~l6_algstr_0(X45))|(v2_struct_0(X44)|~v13_algstr_0(X44)|~v4_vectsp_1(X44)|~v5_vectsp_1(X44)|~v2_rlvect_1(X44)|~v3_rlvect_1(X44)|~v4_rlvect_1(X44)|~v3_group_1(X44)|~l6_algstr_0(X44)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])).
cnf(c_0_72, negated_conjecture, (m1_ring_4(k7_field_16(esk3_0,k1_newton(X1,esk2_0)),esk3_0,u1_struct_0(k12_polynom3(esk3_0)))|v1_zfmisc_1(k1_newton(X1,esk2_0))|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_66, c_0_61])).
cnf(c_0_73, negated_conjecture, (r1_field_4(X1,esk4_0,k7_field_16(X1,k1_newton(esk1_0,esk2_0)),esk5_0)|v1_zfmisc_1(k1_newton(esk1_0,esk2_0))|v6_struct_0(X1)|v2_struct_0(X1)|~v1_field_4(esk4_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)|~v7_ordinal1(k1_newton(esk1_0,esk2_0))), inference(spm,[status(thm)],[c_0_67, c_0_68])).
fof(c_0_74, plain, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>(~v1_zfmisc_1(X1)&v7_ordinal1(X1))), inference(fof_simplification,[status(thm)],[cc1_nat_6])).
fof(c_0_75, plain, ![X41, X42]:(((~v1_zfmisc_1(X42)|(~v7_ordinal1(X42)|~v2_field_16(X42,X41))|(v1_zfmisc_1(X41)|~v7_ordinal1(X41)))&(v7_ordinal1(X42)|(~v7_ordinal1(X42)|~v2_field_16(X42,X41))|(v1_zfmisc_1(X41)|~v7_ordinal1(X41))))&(v2_field_16(X42,X41)|(~v7_ordinal1(X42)|~v2_field_16(X42,X41))|(v1_zfmisc_1(X41)|~v7_ordinal1(X41)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])])).
cnf(c_0_76, plain, (v8_ordinal1(X2)|v2_field_16(k1_newton(X1,X2),X1)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_70])).
cnf(c_0_77, 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_71])).
cnf(c_0_78, negated_conjecture, (m1_ring_4(k7_field_16(esk3_0,k1_newton(esk1_0,esk2_0)),esk3_0,u1_struct_0(k12_polynom3(esk3_0)))|v1_zfmisc_1(k1_newton(esk1_0,esk2_0))), inference(spm,[status(thm)],[c_0_72, c_0_62])).
cnf(c_0_79, negated_conjecture, (r1_field_4(X1,esk4_0,k7_field_16(X1,k1_newton(esk1_0,esk2_0)),esk5_0)|v1_zfmisc_1(k1_newton(esk1_0,esk2_0))|v6_struct_0(X1)|v2_struct_0(X1)|~v1_field_4(esk4_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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_56]), c_0_61]), c_0_62])])).
cnf(c_0_80, negated_conjecture, (v1_field_4(esk4_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
fof(c_0_81, plain, ![X40]:((~v1_zfmisc_1(X40)|(~v7_ordinal1(X40)|~v1_int_2(X40)))&(v7_ordinal1(X40)|(~v7_ordinal1(X40)|~v1_int_2(X40)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])).
cnf(c_0_82, plain, (v1_zfmisc_1(X2)|~v1_zfmisc_1(X1)|~v7_ordinal1(X1)|~v2_field_16(X1,X2)|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_75])).
cnf(c_0_83, negated_conjecture, (v2_field_16(k1_newton(X1,esk2_0),X1)|~v7_ordinal1(X1)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_61]), c_0_63])).
cnf(c_0_84, negated_conjecture, (k1_algnum_1(esk3_0,X1,k7_field_16(esk3_0,k1_newton(esk1_0,esk2_0)),X2)=k4_struct_0(X1)|v1_zfmisc_1(k1_newton(esk1_0,esk2_0))|v2_struct_0(X1)|~r1_field_4(esk3_0,X1,k7_field_16(esk3_0,k1_newton(esk1_0,esk2_0)),X2)|~m1_subset_1(X2,u1_struct_0(X1))|~v1_field_4(X1,esk3_0)|~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_77, c_0_78]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33])]), c_0_35])).
cnf(c_0_85, negated_conjecture, (r1_field_4(esk3_0,esk4_0,k7_field_16(esk3_0,k1_newton(esk1_0,esk2_0)),esk5_0)|v1_zfmisc_1(k1_newton(esk1_0,esk2_0))), 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_79, c_0_80]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33])]), c_0_34]), c_0_35])).
cnf(c_0_86, negated_conjecture, (k1_algnum_1(esk3_0,esk4_0,k7_field_16(esk3_0,k1_newton(esk1_0,esk2_0)),esk5_0)!=k4_struct_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_87, plain, (~v1_zfmisc_1(X1)|~v7_ordinal1(X1)|~v1_int_2(X1)), inference(split_conjunct,[status(thm)],[c_0_81])).
cnf(c_0_88, negated_conjecture, (v1_zfmisc_1(X1)|~v1_zfmisc_1(k1_newton(X1,esk2_0))|~v7_ordinal1(k1_newton(X1,esk2_0))|~v7_ordinal1(X1)), inference(spm,[status(thm)],[c_0_82, c_0_83])).
cnf(c_0_89, negated_conjecture, (v1_zfmisc_1(k1_newton(esk1_0,esk2_0))), 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_41]), c_0_80]), c_0_43]), c_0_45]), c_0_46]), c_0_47]), c_0_48]), c_0_49]), c_0_50]), c_0_52])]), c_0_86]), c_0_54])).
cnf(c_0_90, negated_conjecture, (~v1_zfmisc_1(esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_60]), c_0_62])])).
cnf(c_0_91, negated_conjecture, (~v7_ordinal1(k1_newton(esk1_0,esk2_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_62])]), c_0_90])).
cnf(c_0_92, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_56]), c_0_61]), c_0_62])]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 93
# Proof object clause steps            : 60
# Proof object formula steps           : 33
# Proof object conjectures             : 50
# Proof object clause conjectures      : 47
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 41
# Proof object initial formulas used   : 12
# Proof object generating inferences   : 19
# Proof object simplifying inferences  : 86
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 12
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 53
# Removed in clause preprocessing      : 4
# Initial clauses in saturation        : 49
# Processed clauses                    : 163
# ...of these trivial                  : 0
# ...subsumed                          : 0
# ...remaining for further processing  : 163
# Other redundant clauses eliminated   : 0
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 8
# Backward-rewritten                   : 8
# Generated clauses                    : 160
# ...of the previous two non-trivial   : 158
# Contextual simplify-reflections      : 2
# Paramodulations                      : 159
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 1
# 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  : 147
#    Positive orientable unit clauses  : 33
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 8
#    Non-unit-clauses                  : 106
# Current number of unprocessed clauses: 44
# ...number of literals in the above   : 208
# Current number of archived formulas  : 0
# Current number of archived clauses   : 16
# Clause-clause subsumption calls (NU) : 7691
# Rec. Clause-clause subsumption calls : 1003
# Non-unit clause-clause subsumptions  : 10
# Unit Clause-clause subsumption calls : 151
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 2
# BW rewrite match successes           : 1
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 12110

# -------------------------------------------------
# User time                : 0.040 s
# System time              : 0.004 s
# Total time               : 0.044 s
# Maximum resident set size: 3288 pages
