# 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       : 0.026 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(fc2_ring_4, axiom, ![X1]:((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&v2_ring_4(k12_polynom3(X1),X1))), file('e_trans2/e_trans2__t28_e_trans2', fc2_ring_4)).
fof(fc1_ring_4, axiom, ![X1, X2]:(((((~(v2_struct_0(X1))&l2_struct_0(X1))&~(v2_struct_0(X2)))&v2_ring_4(X2,X1))&l1_struct_0(X2))=>v1_ring_4(u1_struct_0(X2),X1)), file('e_trans2/e_trans2__t28_e_trans2', fc1_ring_4)).
fof(fc4_int_3, axiom, ((((((((~(v6_struct_0(k1_int_3))&v13_algstr_0(k1_int_3))&v3_group_1(k1_int_3))&v5_group_1(k1_int_3))&v2_rlvect_1(k1_int_3))&v3_rlvect_1(k1_int_3))&v4_rlvect_1(k1_int_3))&v5_vectsp_1(k1_int_3))&v1_vectsp_2(k1_int_3)), file('e_trans2/e_trans2__t28_e_trans2', fc4_int_3)).
fof(fc1_int_3, axiom, (~(v2_struct_0(k1_int_3))&v36_algstr_0(k1_int_3)), file('e_trans2/e_trans2__t28_e_trans2', fc1_int_3)).
fof(dt_k1_int_3, axiom, l6_algstr_0(k1_int_3), file('e_trans2/e_trans2__t28_e_trans2', dt_k1_int_3)).
fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('e_trans2/e_trans2__t28_e_trans2', dt_l2_algstr_0)).
fof(dt_l6_algstr_0, axiom, ![X1]:(l6_algstr_0(X1)=>(l2_algstr_0(X1)&l5_algstr_0(X1))), file('e_trans2/e_trans2__t28_e_trans2', dt_l6_algstr_0)).
fof(d1_gcd_1, axiom, ![X1]:((~(v2_struct_0(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(r1_gcd_1(X1,X2,X3)<=>?[X4]:(m1_subset_1(X4,u1_struct_0(X1))&X3=k6_algstr_0(X1,X2,X4)))))), file('e_trans2/e_trans2__t28_e_trans2', d1_gcd_1)).
fof(t28_e_trans2, conjecture, ![X1]:(m1_ring_4(X1,k1_int_3,u1_struct_0(k12_polynom3(k1_int_3)))=>![X2]:(m1_subset_1(X2,u1_struct_0(k1_int_3))=>![X3]:(m1_subset_1(X3,u1_struct_0(k1_int_3))=>r2_tarski(k2_polynom4(k1_int_3,k4_polynom5(k1_int_3,k2_basel_2(k1_int_3,X1),X2),X3),k7_ideal_1(k1_int_3,k1_ring_4(k1_int_3,X2)))))), file('e_trans2/e_trans2__t28_e_trans2', t28_e_trans2)).
fof(redefinition_m1_ring_4, axiom, ![X1, X2]:((((~(v2_struct_0(X1))&l2_struct_0(X1))&~(v1_xboole_0(X2)))&v1_ring_4(X2,X1))=>![X3]:(m1_ring_4(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('e_trans2/e_trans2__t28_e_trans2', redefinition_m1_ring_4)).
fof(dt_k12_polynom3, axiom, ![X1]:((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&l6_algstr_0(k12_polynom3(X1)))), file('e_trans2/e_trans2__t28_e_trans2', dt_k12_polynom3)).
fof(dt_l2_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>l1_struct_0(X1)), file('e_trans2/e_trans2__t28_e_trans2', dt_l2_struct_0)).
fof(dt_l4_algstr_0, axiom, ![X1]:(l4_algstr_0(X1)=>(l3_struct_0(X1)&l3_algstr_0(X1))), file('e_trans2/e_trans2__t28_e_trans2', dt_l4_algstr_0)).
fof(dt_l5_algstr_0, axiom, ![X1]:(l5_algstr_0(X1)=>(l4_algstr_0(X1)&l4_struct_0(X1))), file('e_trans2/e_trans2__t28_e_trans2', dt_l5_algstr_0)).
fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('e_trans2/e_trans2__t28_e_trans2', fc2_struct_0)).
fof(redefinition_k6_domain_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&m1_subset_1(X2,X1))=>k6_domain_1(X1,X2)=k1_tarski(X2)), file('e_trans2/e_trans2__t28_e_trans2', redefinition_k6_domain_1)).
fof(redefinition_r2_gcd_1, axiom, ![X1, X2, X3]:(((((~(v2_struct_0(X1))&v3_vectsp_1(X1))&l4_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))&m1_subset_1(X3,u1_struct_0(X1)))=>(r2_gcd_1(X1,X2,X3)<=>r1_gcd_1(X1,X2,X3))), file('e_trans2/e_trans2__t28_e_trans2', redefinition_r2_gcd_1)).
fof(cc3_vectsp_1, axiom, ![X1]:(l4_algstr_0(X1)=>((~(v2_struct_0(X1))&v4_vectsp_1(X1))=>((~(v2_struct_0(X1))&v3_vectsp_1(X1))&v6_vectsp_1(X1)))), file('e_trans2/e_trans2__t28_e_trans2', cc3_vectsp_1)).
fof(t18_ring_2, 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))&v5_group_1(X1))&l6_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(r2_gcd_1(X1,X2,X3)<=>r2_tarski(X3,k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),X2))))))), file('e_trans2/e_trans2__t28_e_trans2', t18_ring_2)).
fof(dt_k6_algstr_0, axiom, ![X1, X2, X3]:(((l3_algstr_0(X1)&m1_subset_1(X2,u1_struct_0(X1)))&m1_subset_1(X3,u1_struct_0(X1)))=>m1_subset_1(k6_algstr_0(X1,X2,X3),u1_struct_0(X1))), file('e_trans2/e_trans2__t28_e_trans2', dt_k6_algstr_0)).
fof(fc3_int_3, axiom, v4_vectsp_1(k1_int_3), file('e_trans2/e_trans2__t28_e_trans2', fc3_int_3)).
fof(dt_k2_basel_2, axiom, ![X1, X2]:(((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(k12_polynom3(X1))))=>(((v1_funct_1(k2_basel_2(X1,X2))&v1_funct_2(k2_basel_2(X1,X2),k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(k2_basel_2(X1,X2),X1))&m1_subset_1(k2_basel_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), file('e_trans2/e_trans2__t28_e_trans2', dt_k2_basel_2)).
fof(dt_k2_polynom4, axiom, ![X1, X2, X3]:((((((((~(v2_struct_0(X1))&v1_group_1(X1))&l6_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X2,X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))&m1_subset_1(X3,u1_struct_0(X1)))=>m1_subset_1(k2_polynom4(X1,X2,X3),u1_struct_0(X1))), file('e_trans2/e_trans2__t28_e_trans2', dt_k2_polynom4)).
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('e_trans2/e_trans2__t28_e_trans2', cc5_vectsp_1)).
fof(t7_ring_5, axiom, ![X1]:((((((((((((~(v2_struct_0(X1))&~(v6_struct_0(X1)))&v13_algstr_0(X1))&v3_group_1(X1))&v5_group_1(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v1_vectsp_2(X1))&l6_algstr_0(X1))=>![X2]:((((v1_funct_1(X2)&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X2,X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k2_polynom4(X1,k4_polynom5(X1,X2,X3),X4)=k6_algstr_0(X1,X3,k2_polynom4(X1,X2,X4)))))), file('e_trans2/e_trans2__t28_e_trans2', t7_ring_5)).
fof(redefinition_k1_ring_4, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&l6_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))=>k1_ring_4(X1,X2)=k1_tarski(X2)), file('e_trans2/e_trans2__t28_e_trans2', redefinition_k1_ring_4)).
fof(c_0_26, plain, ![X1]:((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&v2_ring_4(k12_polynom3(X1),X1))), inference(fof_simplification,[status(thm)],[fc2_ring_4])).
fof(c_0_27, plain, ![X1, X2]:(((((~v2_struct_0(X1)&l2_struct_0(X1))&~v2_struct_0(X2))&v2_ring_4(X2,X1))&l1_struct_0(X2))=>v1_ring_4(u1_struct_0(X2),X1)), inference(fof_simplification,[status(thm)],[fc1_ring_4])).
fof(c_0_28, plain, ![X75]:(((~v2_struct_0(k12_polynom3(X75))|(v2_struct_0(X75)|~v13_algstr_0(X75)|~v3_rlvect_1(X75)|~v4_rlvect_1(X75)|~v5_vectsp_1(X75)|~l6_algstr_0(X75)))&(v36_algstr_0(k12_polynom3(X75))|(v2_struct_0(X75)|~v13_algstr_0(X75)|~v3_rlvect_1(X75)|~v4_rlvect_1(X75)|~v5_vectsp_1(X75)|~l6_algstr_0(X75))))&(v2_ring_4(k12_polynom3(X75),X75)|(v2_struct_0(X75)|~v13_algstr_0(X75)|~v3_rlvect_1(X75)|~v4_rlvect_1(X75)|~v5_vectsp_1(X75)|~l6_algstr_0(X75)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])).
fof(c_0_29, plain, ((((((((~v6_struct_0(k1_int_3)&v13_algstr_0(k1_int_3))&v3_group_1(k1_int_3))&v5_group_1(k1_int_3))&v2_rlvect_1(k1_int_3))&v3_rlvect_1(k1_int_3))&v4_rlvect_1(k1_int_3))&v5_vectsp_1(k1_int_3))&v1_vectsp_2(k1_int_3)), inference(fof_simplification,[status(thm)],[fc4_int_3])).
fof(c_0_30, plain, (~v2_struct_0(k1_int_3)&v36_algstr_0(k1_int_3)), inference(fof_simplification,[status(thm)],[fc1_int_3])).
fof(c_0_31, plain, ![X73, X74]:(v2_struct_0(X73)|~l2_struct_0(X73)|v2_struct_0(X74)|~v2_ring_4(X74,X73)|~l1_struct_0(X74)|v1_ring_4(u1_struct_0(X74),X73)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])).
cnf(c_0_32, plain, (v2_ring_4(k12_polynom3(X1),X1)|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_28])).
cnf(c_0_33, plain, (l6_algstr_0(k1_int_3)), inference(split_conjunct,[status(thm)],[dt_k1_int_3])).
cnf(c_0_34, plain, (v5_vectsp_1(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_35, plain, (v4_rlvect_1(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_36, plain, (v3_rlvect_1(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_37, plain, (v13_algstr_0(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_38, plain, (~v2_struct_0(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_30])).
fof(c_0_39, plain, ![X68]:((l2_struct_0(X68)|~l2_algstr_0(X68))&(l1_algstr_0(X68)|~l2_algstr_0(X68))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])).
fof(c_0_40, plain, ![X72]:((l2_algstr_0(X72)|~l6_algstr_0(X72))&(l5_algstr_0(X72)|~l6_algstr_0(X72))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])).
fof(c_0_41, plain, ![X1]:((~v2_struct_0(X1)&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(r1_gcd_1(X1,X2,X3)<=>?[X4]:(m1_subset_1(X4,u1_struct_0(X1))&X3=k6_algstr_0(X1,X2,X4)))))), inference(fof_simplification,[status(thm)],[d1_gcd_1])).
fof(c_0_42, negated_conjecture, ~(![X1]:(m1_ring_4(X1,k1_int_3,u1_struct_0(k12_polynom3(k1_int_3)))=>![X2]:(m1_subset_1(X2,u1_struct_0(k1_int_3))=>![X3]:(m1_subset_1(X3,u1_struct_0(k1_int_3))=>r2_tarski(k2_polynom4(k1_int_3,k4_polynom5(k1_int_3,k2_basel_2(k1_int_3,X1),X2),X3),k7_ideal_1(k1_int_3,k1_ring_4(k1_int_3,X2))))))), inference(assume_negation,[status(cth)],[t28_e_trans2])).
fof(c_0_43, plain, ![X1, X2]:((((~v2_struct_0(X1)&l2_struct_0(X1))&~v1_xboole_0(X2))&v1_ring_4(X2,X1))=>![X3]:(m1_ring_4(X3,X1,X2)<=>m1_subset_1(X3,X2))), inference(fof_simplification,[status(thm)],[redefinition_m1_ring_4])).
cnf(c_0_44, plain, (v2_struct_0(X1)|v2_struct_0(X2)|v1_ring_4(u1_struct_0(X2),X1)|~l2_struct_0(X1)|~v2_ring_4(X2,X1)|~l1_struct_0(X2)), inference(split_conjunct,[status(thm)],[c_0_31])).
cnf(c_0_45, plain, (v2_ring_4(k12_polynom3(k1_int_3),k1_int_3)), 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(spm,[status(thm)],[c_0_32, c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_46, plain, (l2_struct_0(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_39])).
cnf(c_0_47, plain, (l2_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_40])).
fof(c_0_48, plain, ![X1]:((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&l6_algstr_0(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[dt_k12_polynom3])).
fof(c_0_49, plain, ![X54, X55, X56, X58]:(((m1_subset_1(esk4_3(X54,X55,X56),u1_struct_0(X54))|~r1_gcd_1(X54,X55,X56)|~m1_subset_1(X56,u1_struct_0(X54))|~m1_subset_1(X55,u1_struct_0(X54))|(v2_struct_0(X54)|~l3_algstr_0(X54)))&(X56=k6_algstr_0(X54,X55,esk4_3(X54,X55,X56))|~r1_gcd_1(X54,X55,X56)|~m1_subset_1(X56,u1_struct_0(X54))|~m1_subset_1(X55,u1_struct_0(X54))|(v2_struct_0(X54)|~l3_algstr_0(X54))))&(~m1_subset_1(X58,u1_struct_0(X54))|X56!=k6_algstr_0(X54,X55,X58)|r1_gcd_1(X54,X55,X56)|~m1_subset_1(X56,u1_struct_0(X54))|~m1_subset_1(X55,u1_struct_0(X54))|(v2_struct_0(X54)|~l3_algstr_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_41])])])])])).
fof(c_0_50, negated_conjecture, (m1_ring_4(esk1_0,k1_int_3,u1_struct_0(k12_polynom3(k1_int_3)))&(m1_subset_1(esk2_0,u1_struct_0(k1_int_3))&(m1_subset_1(esk3_0,u1_struct_0(k1_int_3))&~r2_tarski(k2_polynom4(k1_int_3,k4_polynom5(k1_int_3,k2_basel_2(k1_int_3,esk1_0),esk2_0),esk3_0),k7_ideal_1(k1_int_3,k1_ring_4(k1_int_3,esk2_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])).
fof(c_0_51, plain, ![X81, X82, X83]:((~m1_ring_4(X83,X81,X82)|m1_subset_1(X83,X82)|(v2_struct_0(X81)|~l2_struct_0(X81)|v1_xboole_0(X82)|~v1_ring_4(X82,X81)))&(~m1_subset_1(X83,X82)|m1_ring_4(X83,X81,X82)|(v2_struct_0(X81)|~l2_struct_0(X81)|v1_xboole_0(X82)|~v1_ring_4(X82,X81)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])).
cnf(c_0_52, plain, (v1_ring_4(u1_struct_0(k12_polynom3(k1_int_3)),k1_int_3)|v2_struct_0(k12_polynom3(k1_int_3))|~l1_struct_0(k12_polynom3(k1_int_3))|~l2_struct_0(k1_int_3)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_38])).
cnf(c_0_53, plain, (l2_struct_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_46, c_0_47])).
fof(c_0_54, plain, ![X69]:(~l2_struct_0(X69)|l1_struct_0(X69)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])).
fof(c_0_55, plain, ![X59]:(((~v2_struct_0(k12_polynom3(X59))|(v2_struct_0(X59)|~v13_algstr_0(X59)|~v3_rlvect_1(X59)|~v4_rlvect_1(X59)|~v5_vectsp_1(X59)|~l6_algstr_0(X59)))&(v36_algstr_0(k12_polynom3(X59))|(v2_struct_0(X59)|~v13_algstr_0(X59)|~v3_rlvect_1(X59)|~v4_rlvect_1(X59)|~v5_vectsp_1(X59)|~l6_algstr_0(X59))))&(l6_algstr_0(k12_polynom3(X59))|(v2_struct_0(X59)|~v13_algstr_0(X59)|~v3_rlvect_1(X59)|~v4_rlvect_1(X59)|~v5_vectsp_1(X59)|~l6_algstr_0(X59)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])).
cnf(c_0_56, plain, (r1_gcd_1(X2,X4,X3)|v2_struct_0(X2)|~m1_subset_1(X1,u1_struct_0(X2))|X3!=k6_algstr_0(X2,X4,X1)|~m1_subset_1(X3,u1_struct_0(X2))|~m1_subset_1(X4,u1_struct_0(X2))|~l3_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_57, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(k1_int_3))), inference(split_conjunct,[status(thm)],[c_0_50])).
fof(c_0_58, plain, ![X70]:((l3_struct_0(X70)|~l4_algstr_0(X70))&(l3_algstr_0(X70)|~l4_algstr_0(X70))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l4_algstr_0])])])).
fof(c_0_59, plain, ![X71]:((l4_algstr_0(X71)|~l5_algstr_0(X71))&(l4_struct_0(X71)|~l5_algstr_0(X71))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_algstr_0])])])).
fof(c_0_60, plain, ![X1]:((~v2_struct_0(X1)&l1_struct_0(X1))=>~v1_xboole_0(u1_struct_0(X1))), inference(fof_simplification,[status(thm)],[fc2_struct_0])).
cnf(c_0_61, plain, (m1_subset_1(X1,X3)|v2_struct_0(X2)|v1_xboole_0(X3)|~m1_ring_4(X1,X2,X3)|~l2_struct_0(X2)|~v1_ring_4(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_51])).
cnf(c_0_62, negated_conjecture, (m1_ring_4(esk1_0,k1_int_3,u1_struct_0(k12_polynom3(k1_int_3)))), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_63, plain, (v1_ring_4(u1_struct_0(k12_polynom3(k1_int_3)),k1_int_3)|v2_struct_0(k12_polynom3(k1_int_3))|~l1_struct_0(k12_polynom3(k1_int_3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_33])])).
cnf(c_0_64, plain, (l1_struct_0(X1)|~l2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_54])).
cnf(c_0_65, plain, (l6_algstr_0(k12_polynom3(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_55])).
fof(c_0_66, plain, ![X1, X2]:((~v1_xboole_0(X1)&m1_subset_1(X2,X1))=>k6_domain_1(X1,X2)=k1_tarski(X2)), inference(fof_simplification,[status(thm)],[redefinition_k6_domain_1])).
fof(c_0_67, plain, ![X1, X2, X3]:(((((~v2_struct_0(X1)&v3_vectsp_1(X1))&l4_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))&m1_subset_1(X3,u1_struct_0(X1)))=>(r2_gcd_1(X1,X2,X3)<=>r1_gcd_1(X1,X2,X3))), inference(fof_simplification,[status(thm)],[redefinition_r2_gcd_1])).
cnf(c_0_68, negated_conjecture, (r1_gcd_1(k1_int_3,esk2_0,X1)|X1!=k6_algstr_0(k1_int_3,esk2_0,X2)|~l3_algstr_0(k1_int_3)|~m1_subset_1(X1,u1_struct_0(k1_int_3))|~m1_subset_1(X2,u1_struct_0(k1_int_3))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_38])).
cnf(c_0_69, plain, (l3_algstr_0(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_58])).
cnf(c_0_70, plain, (l4_algstr_0(X1)|~l5_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_59])).
cnf(c_0_71, plain, (l5_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_40])).
fof(c_0_72, plain, ![X1]:(l4_algstr_0(X1)=>((~v2_struct_0(X1)&v4_vectsp_1(X1))=>((~v2_struct_0(X1)&v3_vectsp_1(X1))&v6_vectsp_1(X1)))), inference(fof_simplification,[status(thm)],[cc3_vectsp_1])).
fof(c_0_73, plain, ![X76]:(v2_struct_0(X76)|~l1_struct_0(X76)|~v1_xboole_0(u1_struct_0(X76))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])).
cnf(c_0_74, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k1_int_3)))|m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k1_int_3)))|~v1_ring_4(u1_struct_0(k12_polynom3(k1_int_3)),k1_int_3)|~l2_struct_0(k1_int_3)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_38])).
cnf(c_0_75, plain, (v1_ring_4(u1_struct_0(k12_polynom3(k1_int_3)),k1_int_3)|v2_struct_0(k12_polynom3(k1_int_3))|~l2_struct_0(k12_polynom3(k1_int_3))), inference(spm,[status(thm)],[c_0_63, c_0_64])).
cnf(c_0_76, plain, (l6_algstr_0(k12_polynom3(k1_int_3))), 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(spm,[status(thm)],[c_0_65, c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
fof(c_0_77, 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))&v5_group_1(X1))&l6_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(r2_gcd_1(X1,X2,X3)<=>r2_tarski(X3,k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),X2))))))), inference(fof_simplification,[status(thm)],[t18_ring_2])).
fof(c_0_78, plain, ![X79, X80]:(v1_xboole_0(X79)|~m1_subset_1(X80,X79)|k6_domain_1(X79,X80)=k1_tarski(X80)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])).
fof(c_0_79, plain, ![X84, X85, X86]:((~r2_gcd_1(X84,X85,X86)|r1_gcd_1(X84,X85,X86)|(v2_struct_0(X84)|~v3_vectsp_1(X84)|~l4_algstr_0(X84)|~m1_subset_1(X85,u1_struct_0(X84))|~m1_subset_1(X86,u1_struct_0(X84))))&(~r1_gcd_1(X84,X85,X86)|r2_gcd_1(X84,X85,X86)|(v2_struct_0(X84)|~v3_vectsp_1(X84)|~l4_algstr_0(X84)|~m1_subset_1(X85,u1_struct_0(X84))|~m1_subset_1(X86,u1_struct_0(X84))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])).
fof(c_0_80, plain, ![X65, X66, X67]:(~l3_algstr_0(X65)|~m1_subset_1(X66,u1_struct_0(X65))|~m1_subset_1(X67,u1_struct_0(X65))|m1_subset_1(k6_algstr_0(X65,X66,X67),u1_struct_0(X65))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_algstr_0])])).
cnf(c_0_81, negated_conjecture, (r1_gcd_1(k1_int_3,esk2_0,X1)|X1!=k6_algstr_0(k1_int_3,esk2_0,X2)|~l4_algstr_0(k1_int_3)|~m1_subset_1(X1,u1_struct_0(k1_int_3))|~m1_subset_1(X2,u1_struct_0(k1_int_3))), inference(spm,[status(thm)],[c_0_68, c_0_69])).
cnf(c_0_82, plain, (l4_algstr_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_70, c_0_71])).
fof(c_0_83, plain, ![X52]:(((~v2_struct_0(X52)|(v2_struct_0(X52)|~v4_vectsp_1(X52))|~l4_algstr_0(X52))&(v3_vectsp_1(X52)|(v2_struct_0(X52)|~v4_vectsp_1(X52))|~l4_algstr_0(X52)))&(v6_vectsp_1(X52)|(v2_struct_0(X52)|~v4_vectsp_1(X52))|~l4_algstr_0(X52))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])).
cnf(c_0_84, plain, (v2_struct_0(X1)|~l1_struct_0(X1)|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_73])).
cnf(c_0_85, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k1_int_3)))|m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k1_int_3)))|~v1_ring_4(u1_struct_0(k12_polynom3(k1_int_3)),k1_int_3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_53]), c_0_33])])).
cnf(c_0_86, plain, (v1_ring_4(u1_struct_0(k12_polynom3(k1_int_3)),k1_int_3)|v2_struct_0(k12_polynom3(k1_int_3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_53]), c_0_76])])).
fof(c_0_87, plain, ![X87, X88, X89]:((~r2_gcd_1(X87,X88,X89)|r2_tarski(X89,k7_ideal_1(X87,k6_domain_1(u1_struct_0(X87),X88)))|~m1_subset_1(X89,u1_struct_0(X87))|~m1_subset_1(X88,u1_struct_0(X87))|(v2_struct_0(X87)|~v13_algstr_0(X87)|~v4_vectsp_1(X87)|~v5_vectsp_1(X87)|~v2_rlvect_1(X87)|~v3_rlvect_1(X87)|~v4_rlvect_1(X87)|~v3_group_1(X87)|~v5_group_1(X87)|~l6_algstr_0(X87)))&(~r2_tarski(X89,k7_ideal_1(X87,k6_domain_1(u1_struct_0(X87),X88)))|r2_gcd_1(X87,X88,X89)|~m1_subset_1(X89,u1_struct_0(X87))|~m1_subset_1(X88,u1_struct_0(X87))|(v2_struct_0(X87)|~v13_algstr_0(X87)|~v4_vectsp_1(X87)|~v5_vectsp_1(X87)|~v2_rlvect_1(X87)|~v3_rlvect_1(X87)|~v4_rlvect_1(X87)|~v3_group_1(X87)|~v5_group_1(X87)|~l6_algstr_0(X87)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])])])).
cnf(c_0_88, plain, (v1_xboole_0(X1)|k6_domain_1(X1,X2)=k1_tarski(X2)|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_78])).
cnf(c_0_89, plain, (r2_gcd_1(X1,X2,X3)|v2_struct_0(X1)|~r1_gcd_1(X1,X2,X3)|~v3_vectsp_1(X1)|~l4_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_79])).
cnf(c_0_90, plain, (m1_subset_1(k6_algstr_0(X1,X2,X3),u1_struct_0(X1))|~l3_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_80])).
cnf(c_0_91, negated_conjecture, (r1_gcd_1(k1_int_3,esk2_0,X1)|X1!=k6_algstr_0(k1_int_3,esk2_0,X2)|~m1_subset_1(X1,u1_struct_0(k1_int_3))|~m1_subset_1(X2,u1_struct_0(k1_int_3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_33])])).
cnf(c_0_92, plain, (v3_vectsp_1(X1)|v2_struct_0(X1)|~v4_vectsp_1(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_93, plain, (v4_vectsp_1(k1_int_3)), inference(split_conjunct,[status(thm)],[fc3_int_3])).
fof(c_0_94, plain, ![X1, X2]:(((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(k12_polynom3(X1))))=>(((v1_funct_1(k2_basel_2(X1,X2))&v1_funct_2(k2_basel_2(X1,X2),k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(k2_basel_2(X1,X2),X1))&m1_subset_1(k2_basel_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))), inference(fof_simplification,[status(thm)],[dt_k2_basel_2])).
cnf(c_0_95, plain, (v2_struct_0(X1)|~v1_xboole_0(u1_struct_0(X1))|~l2_struct_0(X1)), inference(spm,[status(thm)],[c_0_84, c_0_64])).
cnf(c_0_96, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(k1_int_3)))|v2_struct_0(k12_polynom3(k1_int_3))|m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k1_int_3)))), inference(spm,[status(thm)],[c_0_85, c_0_86])).
cnf(c_0_97, plain, (r2_tarski(X3,k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),X2)))|v2_struct_0(X1)|~r2_gcd_1(X1,X2,X3)|~m1_subset_1(X3,u1_struct_0(X1))|~m1_subset_1(X2,u1_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)|~v5_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_87])).
cnf(c_0_98, negated_conjecture, (k6_domain_1(u1_struct_0(k1_int_3),esk2_0)=k1_tarski(esk2_0)|v1_xboole_0(u1_struct_0(k1_int_3))), inference(spm,[status(thm)],[c_0_88, c_0_57])).
cnf(c_0_99, plain, (v2_rlvect_1(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_100, plain, (v5_group_1(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_101, plain, (v3_group_1(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_102, plain, (r2_gcd_1(X1,X2,k6_algstr_0(X1,X3,X4))|v2_struct_0(X1)|~r1_gcd_1(X1,X2,k6_algstr_0(X1,X3,X4))|~v3_vectsp_1(X1)|~l4_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))|~m1_subset_1(X4,u1_struct_0(X1))|~m1_subset_1(X3,u1_struct_0(X1))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90]), c_0_69])).
cnf(c_0_103, negated_conjecture, (r1_gcd_1(k1_int_3,esk2_0,k6_algstr_0(k1_int_3,esk2_0,X1))|~m1_subset_1(k6_algstr_0(k1_int_3,esk2_0,X1),u1_struct_0(k1_int_3))|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(er,[status(thm)],[c_0_91])).
cnf(c_0_104, plain, (v3_vectsp_1(k1_int_3)|~l4_algstr_0(k1_int_3)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_93]), c_0_38])).
fof(c_0_105, plain, ![X1, X2, X3]:((((((((~v2_struct_0(X1)&v1_group_1(X1))&l6_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X2,X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))&m1_subset_1(X3,u1_struct_0(X1)))=>m1_subset_1(k2_polynom4(X1,X2,X3),u1_struct_0(X1))), inference(fof_simplification,[status(thm)],[dt_k2_polynom4])).
fof(c_0_106, plain, ![X60, X61]:((((v1_funct_1(k2_basel_2(X60,X61))|(v2_struct_0(X60)|~v13_algstr_0(X60)|~v3_rlvect_1(X60)|~v4_rlvect_1(X60)|~v5_vectsp_1(X60)|~l6_algstr_0(X60)|~m1_subset_1(X61,u1_struct_0(k12_polynom3(X60)))))&(v1_funct_2(k2_basel_2(X60,X61),k4_ordinal1,u1_struct_0(X60))|(v2_struct_0(X60)|~v13_algstr_0(X60)|~v3_rlvect_1(X60)|~v4_rlvect_1(X60)|~v5_vectsp_1(X60)|~l6_algstr_0(X60)|~m1_subset_1(X61,u1_struct_0(k12_polynom3(X60))))))&(v1_polynom1(k2_basel_2(X60,X61),X60)|(v2_struct_0(X60)|~v13_algstr_0(X60)|~v3_rlvect_1(X60)|~v4_rlvect_1(X60)|~v5_vectsp_1(X60)|~l6_algstr_0(X60)|~m1_subset_1(X61,u1_struct_0(k12_polynom3(X60))))))&(m1_subset_1(k2_basel_2(X60,X61),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X60))))|(v2_struct_0(X60)|~v13_algstr_0(X60)|~v3_rlvect_1(X60)|~v4_rlvect_1(X60)|~v5_vectsp_1(X60)|~l6_algstr_0(X60)|~m1_subset_1(X61,u1_struct_0(k12_polynom3(X60)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_94])])])).
cnf(c_0_107, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k1_int_3)))|~l2_struct_0(k12_polynom3(k1_int_3))), inference(spm,[status(thm)],[c_0_95, c_0_96])).
fof(c_0_108, 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_109, plain, ![X1]:((((((((((((~v2_struct_0(X1)&~v6_struct_0(X1))&v13_algstr_0(X1))&v3_group_1(X1))&v5_group_1(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v1_vectsp_2(X1))&l6_algstr_0(X1))=>![X2]:((((v1_funct_1(X2)&v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X2,X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k2_polynom4(X1,k4_polynom5(X1,X2,X3),X4)=k6_algstr_0(X1,X3,k2_polynom4(X1,X2,X4)))))), inference(fof_simplification,[status(thm)],[t7_ring_5])).
cnf(c_0_110, negated_conjecture, (v1_xboole_0(u1_struct_0(k1_int_3))|r2_tarski(X1,k7_ideal_1(k1_int_3,k1_tarski(esk2_0)))|~r2_gcd_1(k1_int_3,esk2_0,X1)|~m1_subset_1(X1,u1_struct_0(k1_int_3))), 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_97, c_0_98]), c_0_99]), c_0_100]), c_0_101]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37]), c_0_93]), c_0_57])]), c_0_38])).
cnf(c_0_111, negated_conjecture, (r2_gcd_1(k1_int_3,esk2_0,k6_algstr_0(k1_int_3,esk2_0,X1))|~l4_algstr_0(k1_int_3)|~m1_subset_1(k6_algstr_0(k1_int_3,esk2_0,X1),u1_struct_0(k1_int_3))|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_57])]), c_0_38]), c_0_104])).
fof(c_0_112, plain, ![X62, X63, X64]:(v2_struct_0(X62)|~v1_group_1(X62)|~l6_algstr_0(X62)|~v1_funct_1(X63)|~v1_funct_2(X63,k4_ordinal1,u1_struct_0(X62))|~v1_polynom1(X63,X62)|~m1_subset_1(X63,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X62))))|~m1_subset_1(X64,u1_struct_0(X62))|m1_subset_1(k2_polynom4(X62,X63,X64),u1_struct_0(X62))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_105])])).
cnf(c_0_113, plain, (m1_subset_1(k2_basel_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_106])).
cnf(c_0_114, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|m1_subset_1(esk1_0,u1_struct_0(k12_polynom3(k1_int_3)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_53]), c_0_76])])).
cnf(c_0_115, plain, (v1_funct_1(k2_basel_2(X1,X2))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_106])).
cnf(c_0_116, plain, (v1_funct_2(k2_basel_2(X1,X2),k4_ordinal1,u1_struct_0(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_106])).
cnf(c_0_117, plain, (v1_polynom1(k2_basel_2(X1,X2),X1)|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_106])).
fof(c_0_118, plain, ![X53]:((~v2_struct_0(X53)|(v2_struct_0(X53)|~v4_vectsp_1(X53))|~l4_algstr_0(X53))&(v1_group_1(X53)|(v2_struct_0(X53)|~v4_vectsp_1(X53))|~l4_algstr_0(X53))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])])])).
fof(c_0_119, plain, ![X1, X2]:(((~v2_struct_0(X1)&l6_algstr_0(X1))&m1_subset_1(X2,u1_struct_0(X1)))=>k1_ring_4(X1,X2)=k1_tarski(X2)), inference(fof_simplification,[status(thm)],[redefinition_k1_ring_4])).
fof(c_0_120, plain, ![X90, X91, X92, X93]:(v2_struct_0(X90)|v6_struct_0(X90)|~v13_algstr_0(X90)|~v3_group_1(X90)|~v5_group_1(X90)|~v2_rlvect_1(X90)|~v3_rlvect_1(X90)|~v4_rlvect_1(X90)|~v4_vectsp_1(X90)|~v5_vectsp_1(X90)|~v1_vectsp_2(X90)|~l6_algstr_0(X90)|(~v1_funct_1(X91)|~v1_funct_2(X91,k4_ordinal1,u1_struct_0(X90))|~v1_polynom1(X91,X90)|~m1_subset_1(X91,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X90))))|(~m1_subset_1(X92,u1_struct_0(X90))|(~m1_subset_1(X93,u1_struct_0(X90))|k2_polynom4(X90,k4_polynom5(X90,X91,X92),X93)=k6_algstr_0(X90,X92,k2_polynom4(X90,X91,X93)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_109])])])).
cnf(c_0_121, negated_conjecture, (v1_xboole_0(u1_struct_0(k1_int_3))|r2_tarski(k6_algstr_0(k1_int_3,esk2_0,X1),k7_ideal_1(k1_int_3,k1_tarski(esk2_0)))|~l4_algstr_0(k1_int_3)|~m1_subset_1(k6_algstr_0(k1_int_3,esk2_0,X1),u1_struct_0(k1_int_3))|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(spm,[status(thm)],[c_0_110, c_0_111])).
cnf(c_0_122, plain, (v2_struct_0(X1)|m1_subset_1(k2_polynom4(X1,X2,X3),u1_struct_0(X1))|~v1_group_1(X1)|~l6_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~v1_polynom1(X2,X1)|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_112])).
cnf(c_0_123, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|m1_subset_1(k2_basel_2(k1_int_3,esk1_0),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_int_3))))), 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_113, c_0_114]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_124, negated_conjecture, (v1_funct_1(k2_basel_2(k1_int_3,esk1_0))|v2_struct_0(k12_polynom3(k1_int_3))), 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_115, c_0_114]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_125, negated_conjecture, (v1_funct_2(k2_basel_2(k1_int_3,esk1_0),k4_ordinal1,u1_struct_0(k1_int_3))|v2_struct_0(k12_polynom3(k1_int_3))), 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_116, c_0_114]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_126, negated_conjecture, (v1_polynom1(k2_basel_2(k1_int_3,esk1_0),k1_int_3)|v2_struct_0(k12_polynom3(k1_int_3))), 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_117, c_0_114]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38])).
cnf(c_0_127, plain, (v1_group_1(X1)|v2_struct_0(X1)|~v4_vectsp_1(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_118])).
fof(c_0_128, plain, ![X77, X78]:(v2_struct_0(X77)|~l6_algstr_0(X77)|~m1_subset_1(X78,u1_struct_0(X77))|k1_ring_4(X77,X78)=k1_tarski(X78)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])).
cnf(c_0_129, plain, (v2_struct_0(X1)|v6_struct_0(X1)|k2_polynom4(X1,k4_polynom5(X1,X2,X3),X4)=k6_algstr_0(X1,X3,k2_polynom4(X1,X2,X4))|~v13_algstr_0(X1)|~v3_group_1(X1)|~v5_group_1(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v1_vectsp_2(X1)|~l6_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,k4_ordinal1,u1_struct_0(X1))|~v1_polynom1(X2,X1)|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))|~m1_subset_1(X3,u1_struct_0(X1))|~m1_subset_1(X4,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_120])).
cnf(c_0_130, plain, (v1_vectsp_2(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_131, plain, (~v6_struct_0(k1_int_3)), inference(split_conjunct,[status(thm)],[c_0_29])).
cnf(c_0_132, negated_conjecture, (v1_xboole_0(u1_struct_0(k1_int_3))|r2_tarski(k6_algstr_0(k1_int_3,esk2_0,X1),k7_ideal_1(k1_int_3,k1_tarski(esk2_0)))|~m1_subset_1(k6_algstr_0(k1_int_3,esk2_0,X1),u1_struct_0(k1_int_3))|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_82]), c_0_33])])).
cnf(c_0_133, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|m1_subset_1(k2_polynom4(k1_int_3,k2_basel_2(k1_int_3,esk1_0),X1),u1_struct_0(k1_int_3))|~v1_group_1(k1_int_3)|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123]), c_0_33])]), c_0_38]), c_0_124]), c_0_125]), c_0_126])).
cnf(c_0_134, plain, (v1_group_1(k1_int_3)|~l4_algstr_0(k1_int_3)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_93]), c_0_38])).
cnf(c_0_135, plain, (v2_struct_0(X1)|k1_ring_4(X1,X2)=k1_tarski(X2)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_128])).
cnf(c_0_136, negated_conjecture, (k2_polynom4(k1_int_3,k4_polynom5(k1_int_3,k2_basel_2(k1_int_3,esk1_0),X1),X2)=k6_algstr_0(k1_int_3,X1,k2_polynom4(k1_int_3,k2_basel_2(k1_int_3,esk1_0),X2))|v2_struct_0(k12_polynom3(k1_int_3))|~m1_subset_1(X2,u1_struct_0(k1_int_3))|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_123]), c_0_130]), c_0_99]), c_0_100]), c_0_101]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37]), c_0_93])]), c_0_131]), c_0_38]), c_0_124]), c_0_125]), c_0_126])).
cnf(c_0_137, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(k1_int_3))), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_138, negated_conjecture, (v1_xboole_0(u1_struct_0(k1_int_3))|r2_tarski(k6_algstr_0(k1_int_3,esk2_0,X1),k7_ideal_1(k1_int_3,k1_tarski(esk2_0)))|~l3_algstr_0(k1_int_3)|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_90]), c_0_57])])).
cnf(c_0_139, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|m1_subset_1(k2_polynom4(k1_int_3,k2_basel_2(k1_int_3,esk1_0),X1),u1_struct_0(k1_int_3))|~l4_algstr_0(k1_int_3)|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(spm,[status(thm)],[c_0_133, c_0_134])).
cnf(c_0_140, negated_conjecture, (~r2_tarski(k2_polynom4(k1_int_3,k4_polynom5(k1_int_3,k2_basel_2(k1_int_3,esk1_0),esk2_0),esk3_0),k7_ideal_1(k1_int_3,k1_ring_4(k1_int_3,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_141, negated_conjecture, (k1_ring_4(k1_int_3,esk2_0)=k1_tarski(esk2_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_57]), c_0_33])]), c_0_38])).
cnf(c_0_142, negated_conjecture, (k2_polynom4(k1_int_3,k4_polynom5(k1_int_3,k2_basel_2(k1_int_3,esk1_0),X1),esk3_0)=k6_algstr_0(k1_int_3,X1,k2_polynom4(k1_int_3,k2_basel_2(k1_int_3,esk1_0),esk3_0))|v2_struct_0(k12_polynom3(k1_int_3))|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(spm,[status(thm)],[c_0_136, c_0_137])).
cnf(c_0_143, negated_conjecture, (v1_xboole_0(u1_struct_0(k1_int_3))|r2_tarski(k6_algstr_0(k1_int_3,esk2_0,X1),k7_ideal_1(k1_int_3,k1_tarski(esk2_0)))|~l4_algstr_0(k1_int_3)|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(spm,[status(thm)],[c_0_138, c_0_69])).
cnf(c_0_144, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|m1_subset_1(k2_polynom4(k1_int_3,k2_basel_2(k1_int_3,esk1_0),X1),u1_struct_0(k1_int_3))|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_82]), c_0_33])])).
cnf(c_0_145, negated_conjecture, (~r2_tarski(k2_polynom4(k1_int_3,k4_polynom5(k1_int_3,k2_basel_2(k1_int_3,esk1_0),esk2_0),esk3_0),k7_ideal_1(k1_int_3,k1_tarski(esk2_0)))), inference(rw,[status(thm)],[c_0_140, c_0_141])).
cnf(c_0_146, negated_conjecture, (k2_polynom4(k1_int_3,k4_polynom5(k1_int_3,k2_basel_2(k1_int_3,esk1_0),esk2_0),esk3_0)=k6_algstr_0(k1_int_3,esk2_0,k2_polynom4(k1_int_3,k2_basel_2(k1_int_3,esk1_0),esk3_0))|v2_struct_0(k12_polynom3(k1_int_3))), inference(spm,[status(thm)],[c_0_142, c_0_57])).
cnf(c_0_147, negated_conjecture, (v1_xboole_0(u1_struct_0(k1_int_3))|r2_tarski(k6_algstr_0(k1_int_3,esk2_0,X1),k7_ideal_1(k1_int_3,k1_tarski(esk2_0)))|~m1_subset_1(X1,u1_struct_0(k1_int_3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143, c_0_82]), c_0_33])])).
cnf(c_0_148, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|m1_subset_1(k2_polynom4(k1_int_3,k2_basel_2(k1_int_3,esk1_0),esk3_0),u1_struct_0(k1_int_3))), inference(spm,[status(thm)],[c_0_144, c_0_137])).
cnf(c_0_149, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|~r2_tarski(k6_algstr_0(k1_int_3,esk2_0,k2_polynom4(k1_int_3,k2_basel_2(k1_int_3,esk1_0),esk3_0)),k7_ideal_1(k1_int_3,k1_tarski(esk2_0)))), inference(spm,[status(thm)],[c_0_145, c_0_146])).
cnf(c_0_150, negated_conjecture, (v1_xboole_0(u1_struct_0(k1_int_3))|v2_struct_0(k12_polynom3(k1_int_3))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147, c_0_148]), c_0_149])).
cnf(c_0_151, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))|~l2_struct_0(k1_int_3)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_150]), c_0_38])).
cnf(c_0_152, plain, (v2_struct_0(X1)|~v2_struct_0(k12_polynom3(X1))|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_55])).
cnf(c_0_153, negated_conjecture, (v2_struct_0(k12_polynom3(k1_int_3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151, c_0_53]), c_0_33])])).
cnf(c_0_154, negated_conjecture, ($false), 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_152, c_0_153]), c_0_33]), c_0_34]), c_0_35]), c_0_36]), c_0_37])]), c_0_38]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 155
# Proof object clause steps            : 89
# Proof object formula steps           : 66
# Proof object conjectures             : 42
# Proof object clause conjectures      : 39
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 42
# Proof object initial formulas used   : 26
# Proof object generating inferences   : 46
# Proof object simplifying inferences  : 117
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 26
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 57
# Removed in clause preprocessing      : 2
# Initial clauses in saturation        : 55
# Processed clauses                    : 986
# ...of these trivial                  : 0
# ...subsumed                          : 149
# ...remaining for further processing  : 837
# Other redundant clauses eliminated   : 14
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 227
# Backward-rewritten                   : 288
# Generated clauses                    : 3933
# ...of the previous two non-trivial   : 3822
# Contextual simplify-reflections      : 109
# Paramodulations                      : 3912
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 21
# 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  : 269
#    Positive orientable unit clauses  : 20
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 3
#    Non-unit-clauses                  : 246
# Current number of unprocessed clauses: 2936
# ...number of literals in the above   : 13054
# Current number of archived formulas  : 0
# Current number of archived clauses   : 568
# Clause-clause subsumption calls (NU) : 83109
# Rec. Clause-clause subsumption calls : 18630
# Non-unit clause-clause subsumptions  : 485
# Unit Clause-clause subsumption calls : 16
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 2
# BW rewrite match successes           : 2
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 233069

# -------------------------------------------------
# User time                : 0.150 s
# System time              : 0.008 s
# Total time               : 0.158 s
# Maximum resident set size: 3316 pages
