# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
# and selection function SelectComplexExceptUniqMaxHorn.
#
# Preprocessing time       : 0.031 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
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__l49_e_trans2', redefinition_m1_ring_4)).
fof(l49_e_trans2, conjecture, ![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]:(v7_ordinal1(X2)=>![X3]:(m1_ring_4(X3,X1,u1_struct_0(k12_polynom3(X1)))=>k8_ringder1(X1,k1_vectsp11(k12_polynom3(X1),k9_ringder1(X1),k5_numbers),k2_binom(k12_polynom3(X1),X3,X2))=k2_binom(k12_polynom3(X1),X3,X2)))), file('e_trans2/e_trans2__l49_e_trans2', l49_e_trans2)).
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__l49_e_trans2', fc2_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__l49_e_trans2', dt_k12_polynom3)).
fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('e_trans2/e_trans2__l49_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__l49_e_trans2', dt_l6_algstr_0)).
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__l49_e_trans2', fc1_ring_4)).
fof(redefinition_r2_funct_2, axiom, ![X1, X2, X3, X4]:((((((v1_funct_1(X3)&v1_funct_2(X3,X1,X2))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&v1_funct_1(X4))&v1_funct_2(X4,X1,X2))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(r2_funct_2(X1,X2,X3,X4)<=>X3=X4)), file('e_trans2/e_trans2__l49_e_trans2', redefinition_r2_funct_2)).
fof(dt_k3_struct_0, axiom, ![X1]:(l1_struct_0(X1)=>((v1_funct_1(k3_struct_0(X1))&v1_funct_2(k3_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(k3_struct_0(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))), file('e_trans2/e_trans2__l49_e_trans2', dt_k3_struct_0)).
fof(t18_vectsp11, axiom, ![X1]:(l1_struct_0(X1)=>![X2]:(((v1_funct_1(X2)&v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))=>r2_funct_2(u1_struct_0(X1),u1_struct_0(X1),k1_vectsp11(X1,X2,k5_numbers),k3_struct_0(X1)))), file('e_trans2/e_trans2__l49_e_trans2', t18_vectsp11)).
fof(dt_l2_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>l1_struct_0(X1)), file('e_trans2/e_trans2__l49_e_trans2', dt_l2_struct_0)).
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__l49_e_trans2', cc5_vectsp_1)).
fof(dt_l5_algstr_0, axiom, ![X1]:(l5_algstr_0(X1)=>(l4_algstr_0(X1)&l4_struct_0(X1))), file('e_trans2/e_trans2__l49_e_trans2', dt_l5_algstr_0)).
fof(dt_k1_vectsp11, axiom, ![X1, X2, X3]:(((((l1_struct_0(X1)&v1_funct_1(X2))&v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))&v7_ordinal1(X3))=>((v1_funct_1(k1_vectsp11(X1,X2,X3))&v1_funct_2(k1_vectsp11(X1,X2,X3),u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(k1_vectsp11(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))), file('e_trans2/e_trans2__l49_e_trans2', dt_k1_vectsp11)).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1), file('e_trans2/e_trans2__l49_e_trans2', fc8_ordinal1)).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1, file('e_trans2/e_trans2__l49_e_trans2', redefinition_k5_numbers)).
fof(dt_k9_ringder1, axiom, ![X1]:(((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_group_1(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((v1_funct_1(k9_ringder1(X1))&v1_funct_2(k9_ringder1(X1),u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1))))&m1_subset_1(k9_ringder1(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1))))))), file('e_trans2/e_trans2__l49_e_trans2', dt_k9_ringder1)).
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__l49_e_trans2', fc2_struct_0)).
fof(fc3_ring_4, axiom, ![X1]:(((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&v4_vectsp_1(k12_polynom3(X1)))), file('e_trans2/e_trans2__l49_e_trans2', fc3_ring_4)).
fof(redefinition_k8_ringder1, axiom, ![X1, X2, X3]:(((((((((((((((~(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))&l6_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1))))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1))))))&m1_subset_1(X3,u1_struct_0(k12_polynom3(X1))))=>k8_ringder1(X1,X2,X3)=k1_funct_1(X2,X3)), file('e_trans2/e_trans2__l49_e_trans2', redefinition_k8_ringder1)).
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('e_trans2/e_trans2__l49_e_trans2', dt_k2_binom)).
fof(rd1_funct_1, axiom, ![X1, X2]:(m1_subset_1(X2,X1)=>k1_funct_1(k4_relat_1(X1),X2)=X2), file('e_trans2/e_trans2__l49_e_trans2', rd1_funct_1)).
fof(redefinition_k6_partfun1, axiom, ![X1]:k6_partfun1(X1)=k4_relat_1(X1), file('e_trans2/e_trans2__l49_e_trans2', redefinition_k6_partfun1)).
fof(d4_struct_0, axiom, ![X1]:(l1_struct_0(X1)=>k3_struct_0(X1)=k6_partfun1(u1_struct_0(X1))), file('e_trans2/e_trans2__l49_e_trans2', d4_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__l49_e_trans2', dt_l4_algstr_0)).
fof(c_0_25, 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])).
fof(c_0_26, negated_conjecture, ~(![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]:(v7_ordinal1(X2)=>![X3]:(m1_ring_4(X3,X1,u1_struct_0(k12_polynom3(X1)))=>k8_ringder1(X1,k1_vectsp11(k12_polynom3(X1),k9_ringder1(X1),k5_numbers),k2_binom(k12_polynom3(X1),X3,X2))=k2_binom(k12_polynom3(X1),X3,X2))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l49_e_trans2])])).
fof(c_0_27, 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_28, 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_29, plain, ![X74, X75, X76]:((~m1_ring_4(X76,X74,X75)|m1_subset_1(X76,X75)|(v2_struct_0(X74)|~l2_struct_0(X74)|v1_xboole_0(X75)|~v1_ring_4(X75,X74)))&(~m1_subset_1(X76,X75)|m1_ring_4(X76,X74,X75)|(v2_struct_0(X74)|~l2_struct_0(X74)|v1_xboole_0(X75)|~v1_ring_4(X75,X74)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])).
fof(c_0_30, negated_conjecture, ((((((((((((~v2_struct_0(esk1_0)&~v6_struct_0(esk1_0))&v13_algstr_0(esk1_0))&v3_group_1(esk1_0))&v5_group_1(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_vectsp_2(esk1_0))&l6_algstr_0(esk1_0))&(v7_ordinal1(esk2_0)&(m1_ring_4(esk3_0,esk1_0,u1_struct_0(k12_polynom3(esk1_0)))&k8_ringder1(esk1_0,k1_vectsp11(k12_polynom3(esk1_0),k9_ringder1(esk1_0),k5_numbers),k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0))!=k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])).
fof(c_0_31, plain, ![X58]:((l2_struct_0(X58)|~l2_algstr_0(X58))&(l1_algstr_0(X58)|~l2_algstr_0(X58))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])).
fof(c_0_32, plain, ![X62]:((l2_algstr_0(X62)|~l6_algstr_0(X62))&(l5_algstr_0(X62)|~l6_algstr_0(X62))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])).
fof(c_0_33, 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_34, plain, ![X65]:(((~v2_struct_0(k12_polynom3(X65))|(v2_struct_0(X65)|~v13_algstr_0(X65)|~v3_rlvect_1(X65)|~v4_rlvect_1(X65)|~v5_vectsp_1(X65)|~l6_algstr_0(X65)))&(v36_algstr_0(k12_polynom3(X65))|(v2_struct_0(X65)|~v13_algstr_0(X65)|~v3_rlvect_1(X65)|~v4_rlvect_1(X65)|~v5_vectsp_1(X65)|~l6_algstr_0(X65))))&(v2_ring_4(k12_polynom3(X65),X65)|(v2_struct_0(X65)|~v13_algstr_0(X65)|~v3_rlvect_1(X65)|~v4_rlvect_1(X65)|~v5_vectsp_1(X65)|~l6_algstr_0(X65)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])).
fof(c_0_35, plain, ![X49]:(((~v2_struct_0(k12_polynom3(X49))|(v2_struct_0(X49)|~v13_algstr_0(X49)|~v3_rlvect_1(X49)|~v4_rlvect_1(X49)|~v5_vectsp_1(X49)|~l6_algstr_0(X49)))&(v36_algstr_0(k12_polynom3(X49))|(v2_struct_0(X49)|~v13_algstr_0(X49)|~v3_rlvect_1(X49)|~v4_rlvect_1(X49)|~v5_vectsp_1(X49)|~l6_algstr_0(X49))))&(l6_algstr_0(k12_polynom3(X49))|(v2_struct_0(X49)|~v13_algstr_0(X49)|~v3_rlvect_1(X49)|~v4_rlvect_1(X49)|~v5_vectsp_1(X49)|~l6_algstr_0(X49)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])).
cnf(c_0_36, 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_29])).
cnf(c_0_37, negated_conjecture, (m1_ring_4(esk3_0,esk1_0,u1_struct_0(k12_polynom3(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_38, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_39, plain, (l2_struct_0(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_31])).
cnf(c_0_40, plain, (l2_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_32])).
fof(c_0_41, plain, ![X63, X64]:(v2_struct_0(X63)|~l2_struct_0(X63)|v2_struct_0(X64)|~v2_ring_4(X64,X63)|~l1_struct_0(X64)|v1_ring_4(u1_struct_0(X64),X63)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])).
cnf(c_0_42, 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_34])).
cnf(c_0_43, negated_conjecture, (l6_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_44, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_45, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_46, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_47, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_48, 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_35])).
fof(c_0_49, plain, ![X77, X78, X79, X80]:((~r2_funct_2(X77,X78,X79,X80)|X79=X80|(~v1_funct_1(X79)|~v1_funct_2(X79,X77,X78)|~m1_subset_1(X79,k1_zfmisc_1(k2_zfmisc_1(X77,X78)))|~v1_funct_1(X80)|~v1_funct_2(X80,X77,X78)|~m1_subset_1(X80,k1_zfmisc_1(k2_zfmisc_1(X77,X78)))))&(X79!=X80|r2_funct_2(X77,X78,X79,X80)|(~v1_funct_1(X79)|~v1_funct_2(X79,X77,X78)|~m1_subset_1(X79,k1_zfmisc_1(k2_zfmisc_1(X77,X78)))|~v1_funct_1(X80)|~v1_funct_2(X80,X77,X78)|~m1_subset_1(X80,k1_zfmisc_1(k2_zfmisc_1(X77,X78)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r2_funct_2])])])).
fof(c_0_50, plain, ![X56]:(((v1_funct_1(k3_struct_0(X56))|~l1_struct_0(X56))&(v1_funct_2(k3_struct_0(X56),u1_struct_0(X56),u1_struct_0(X56))|~l1_struct_0(X56)))&(m1_subset_1(k3_struct_0(X56),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X56),u1_struct_0(X56))))|~l1_struct_0(X56))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_struct_0])])])).
cnf(c_0_51, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|m1_subset_1(esk3_0,u1_struct_0(k12_polynom3(esk1_0)))|~v1_ring_4(u1_struct_0(k12_polynom3(esk1_0)),esk1_0)|~l2_struct_0(esk1_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_38])).
cnf(c_0_52, plain, (l2_struct_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_39, c_0_40])).
cnf(c_0_53, 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_41])).
cnf(c_0_54, negated_conjecture, (v2_ring_4(k12_polynom3(esk1_0),esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_44]), c_0_45]), c_0_46]), c_0_47])]), c_0_38])).
cnf(c_0_55, negated_conjecture, (~v2_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(spm,[status(thm)],[c_0_48, c_0_44]), c_0_43]), c_0_45]), c_0_46]), c_0_47])]), c_0_38])).
cnf(c_0_56, plain, (X3=X4|~r2_funct_2(X1,X2,X3,X4)|~v1_funct_1(X3)|~v1_funct_2(X3,X1,X2)|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))|~v1_funct_1(X4)|~v1_funct_2(X4,X1,X2)|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_49])).
cnf(c_0_57, plain, (m1_subset_1(k3_struct_0(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_58, plain, (v1_funct_1(k3_struct_0(X1))|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_59, plain, (v1_funct_2(k3_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1))|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
fof(c_0_60, plain, ![X81, X82]:(~l1_struct_0(X81)|(~v1_funct_1(X82)|~v1_funct_2(X82,u1_struct_0(X81),u1_struct_0(X81))|~m1_subset_1(X82,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X81),u1_struct_0(X81))))|r2_funct_2(u1_struct_0(X81),u1_struct_0(X81),k1_vectsp11(X81,X82,k5_numbers),k3_struct_0(X81)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t18_vectsp11])])])).
cnf(c_0_61, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|m1_subset_1(esk3_0,u1_struct_0(k12_polynom3(esk1_0)))|~v1_ring_4(u1_struct_0(k12_polynom3(esk1_0)),esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_43])])).
cnf(c_0_62, negated_conjecture, (v1_ring_4(u1_struct_0(k12_polynom3(esk1_0)),esk1_0)|~l2_struct_0(esk1_0)|~l1_struct_0(k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_55]), c_0_38])).
fof(c_0_63, plain, ![X59]:(~l2_struct_0(X59)|l1_struct_0(X59)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])).
fof(c_0_64, 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_65, plain, ![X61]:((l4_algstr_0(X61)|~l5_algstr_0(X61))&(l4_struct_0(X61)|~l5_algstr_0(X61))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_algstr_0])])])).
cnf(c_0_66, plain, (X1=k3_struct_0(X2)|~r2_funct_2(u1_struct_0(X2),u1_struct_0(X2),X1,k3_struct_0(X2))|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2))))|~v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))|~v1_funct_1(X1)|~l1_struct_0(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58]), c_0_59])).
cnf(c_0_67, plain, (r2_funct_2(u1_struct_0(X1),u1_struct_0(X1),k1_vectsp11(X1,X2,k5_numbers),k3_struct_0(X1))|~l1_struct_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))), inference(split_conjunct,[status(thm)],[c_0_60])).
fof(c_0_68, plain, ![X50, X51, X52]:(((v1_funct_1(k1_vectsp11(X50,X51,X52))|(~l1_struct_0(X50)|~v1_funct_1(X51)|~v1_funct_2(X51,u1_struct_0(X50),u1_struct_0(X50))|~m1_subset_1(X51,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X50),u1_struct_0(X50))))|~v7_ordinal1(X52)))&(v1_funct_2(k1_vectsp11(X50,X51,X52),u1_struct_0(X50),u1_struct_0(X50))|(~l1_struct_0(X50)|~v1_funct_1(X51)|~v1_funct_2(X51,u1_struct_0(X50),u1_struct_0(X50))|~m1_subset_1(X51,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X50),u1_struct_0(X50))))|~v7_ordinal1(X52))))&(m1_subset_1(k1_vectsp11(X50,X51,X52),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X50),u1_struct_0(X50))))|(~l1_struct_0(X50)|~v1_funct_1(X51)|~v1_funct_2(X51,u1_struct_0(X50),u1_struct_0(X50))|~m1_subset_1(X51,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X50),u1_struct_0(X50))))|~v7_ordinal1(X52)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_vectsp11])])])).
cnf(c_0_69, plain, (v7_ordinal1(k5_ordinal1)), inference(split_conjunct,[status(thm)],[fc8_ordinal1])).
cnf(c_0_70, plain, (k5_numbers=k5_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])).
fof(c_0_71, plain, ![X1]:(((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_group_1(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((v1_funct_1(k9_ringder1(X1))&v1_funct_2(k9_ringder1(X1),u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1))))&m1_subset_1(k9_ringder1(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1))))))), inference(fof_simplification,[status(thm)],[dt_k9_ringder1])).
fof(c_0_72, 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_73, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|m1_subset_1(esk3_0,u1_struct_0(k12_polynom3(esk1_0)))|~l2_struct_0(esk1_0)|~l1_struct_0(k12_polynom3(esk1_0))), inference(spm,[status(thm)],[c_0_61, c_0_62])).
cnf(c_0_74, plain, (l1_struct_0(X1)|~l2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_63])).
cnf(c_0_75, 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_35])).
fof(c_0_76, plain, ![X47]:((~v2_struct_0(X47)|(v2_struct_0(X47)|~v4_vectsp_1(X47))|~l4_algstr_0(X47))&(v1_group_1(X47)|(v2_struct_0(X47)|~v4_vectsp_1(X47))|~l4_algstr_0(X47))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])).
cnf(c_0_77, plain, (l4_algstr_0(X1)|~l5_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_65])).
cnf(c_0_78, plain, (l5_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_32])).
fof(c_0_79, plain, ![X1]:(((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&v4_vectsp_1(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc3_ring_4])).
cnf(c_0_80, plain, (k1_vectsp11(X1,X2,k5_numbers)=k3_struct_0(X1)|~m1_subset_1(k1_vectsp11(X1,X2,k5_numbers),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~v1_funct_2(k1_vectsp11(X1,X2,k5_numbers),u1_struct_0(X1),u1_struct_0(X1))|~v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))|~v1_funct_1(k1_vectsp11(X1,X2,k5_numbers))|~v1_funct_1(X2)|~l1_struct_0(X1)), inference(spm,[status(thm)],[c_0_66, c_0_67])).
cnf(c_0_81, plain, (m1_subset_1(k1_vectsp11(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~l1_struct_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~v7_ordinal1(X3)), inference(split_conjunct,[status(thm)],[c_0_68])).
cnf(c_0_82, plain, (v7_ordinal1(k5_numbers)), inference(rw,[status(thm)],[c_0_69, c_0_70])).
fof(c_0_83, plain, ![X57]:(((v1_funct_1(k9_ringder1(X57))|(v2_struct_0(X57)|~v13_algstr_0(X57)|~v3_group_1(X57)|~v2_rlvect_1(X57)|~v3_rlvect_1(X57)|~v4_rlvect_1(X57)|~v4_vectsp_1(X57)|~v5_vectsp_1(X57)|~l6_algstr_0(X57)))&(v1_funct_2(k9_ringder1(X57),u1_struct_0(k12_polynom3(X57)),u1_struct_0(k12_polynom3(X57)))|(v2_struct_0(X57)|~v13_algstr_0(X57)|~v3_group_1(X57)|~v2_rlvect_1(X57)|~v3_rlvect_1(X57)|~v4_rlvect_1(X57)|~v4_vectsp_1(X57)|~v5_vectsp_1(X57)|~l6_algstr_0(X57))))&(m1_subset_1(k9_ringder1(X57),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(X57)),u1_struct_0(k12_polynom3(X57)))))|(v2_struct_0(X57)|~v13_algstr_0(X57)|~v3_group_1(X57)|~v2_rlvect_1(X57)|~v3_rlvect_1(X57)|~v4_rlvect_1(X57)|~v4_vectsp_1(X57)|~v5_vectsp_1(X57)|~l6_algstr_0(X57)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])).
fof(c_0_84, plain, ![X66]:(v2_struct_0(X66)|~l1_struct_0(X66)|~v1_xboole_0(u1_struct_0(X66))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])).
cnf(c_0_85, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|m1_subset_1(esk3_0,u1_struct_0(k12_polynom3(esk1_0)))|~l1_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_52]), c_0_43])])).
cnf(c_0_86, plain, (l1_struct_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_74, c_0_52])).
cnf(c_0_87, negated_conjecture, (l6_algstr_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(spm,[status(thm)],[c_0_75, c_0_43]), c_0_44]), c_0_45]), c_0_46]), c_0_47])]), c_0_38])).
cnf(c_0_88, plain, (v1_group_1(X1)|v2_struct_0(X1)|~v4_vectsp_1(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_76])).
cnf(c_0_89, plain, (l4_algstr_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_77, c_0_78])).
fof(c_0_90, plain, ![X67]:(((~v2_struct_0(k12_polynom3(X67))|(v2_struct_0(X67)|~v13_algstr_0(X67)|~v3_rlvect_1(X67)|~v4_rlvect_1(X67)|~v4_vectsp_1(X67)|~v5_vectsp_1(X67)|~l6_algstr_0(X67)))&(v36_algstr_0(k12_polynom3(X67))|(v2_struct_0(X67)|~v13_algstr_0(X67)|~v3_rlvect_1(X67)|~v4_rlvect_1(X67)|~v4_vectsp_1(X67)|~v5_vectsp_1(X67)|~l6_algstr_0(X67))))&(v4_vectsp_1(k12_polynom3(X67))|(v2_struct_0(X67)|~v13_algstr_0(X67)|~v3_rlvect_1(X67)|~v4_rlvect_1(X67)|~v4_vectsp_1(X67)|~v5_vectsp_1(X67)|~l6_algstr_0(X67)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])])).
cnf(c_0_91, plain, (k1_vectsp11(X1,X2,k5_numbers)=k3_struct_0(X1)|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~v1_funct_2(k1_vectsp11(X1,X2,k5_numbers),u1_struct_0(X1),u1_struct_0(X1))|~v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))|~v1_funct_1(k1_vectsp11(X1,X2,k5_numbers))|~v1_funct_1(X2)|~l1_struct_0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_81]), c_0_82])])).
cnf(c_0_92, plain, (v1_funct_2(k1_vectsp11(X1,X2,X3),u1_struct_0(X1),u1_struct_0(X1))|~l1_struct_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~v7_ordinal1(X3)), inference(split_conjunct,[status(thm)],[c_0_68])).
cnf(c_0_93, plain, (m1_subset_1(k9_ringder1(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1)))))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_group_1(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_94, negated_conjecture, (v4_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_95, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_96, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_97, plain, (v1_funct_2(k9_ringder1(X1),u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1)))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_group_1(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_83])).
cnf(c_0_98, plain, (v1_funct_1(k9_ringder1(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_group_1(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_83])).
fof(c_0_99, plain, ![X1, X2, X3]:(((((((((((((((~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))&l6_algstr_0(X1))&v1_funct_1(X2))&v1_funct_2(X2,u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1))))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1))))))&m1_subset_1(X3,u1_struct_0(k12_polynom3(X1))))=>k8_ringder1(X1,X2,X3)=k1_funct_1(X2,X3)), inference(fof_simplification,[status(thm)],[redefinition_k8_ringder1])).
fof(c_0_100, 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])).
cnf(c_0_101, plain, (v2_struct_0(X1)|~l1_struct_0(X1)|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_84])).
cnf(c_0_102, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|m1_subset_1(esk3_0,u1_struct_0(k12_polynom3(esk1_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86]), c_0_87])])).
cnf(c_0_103, plain, (v1_group_1(X1)|v2_struct_0(X1)|~l6_algstr_0(X1)|~v4_vectsp_1(X1)), inference(spm,[status(thm)],[c_0_88, c_0_89])).
cnf(c_0_104, plain, (v4_vectsp_1(k12_polynom3(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_90])).
cnf(c_0_105, plain, (k1_vectsp11(X1,X2,k5_numbers)=k3_struct_0(X1)|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))|~v1_funct_1(k1_vectsp11(X1,X2,k5_numbers))|~v1_funct_1(X2)|~l1_struct_0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92]), c_0_82])])).
cnf(c_0_106, negated_conjecture, (m1_subset_1(k9_ringder1(esk1_0),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(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(spm,[status(thm)],[c_0_93, c_0_43]), c_0_44]), c_0_94]), c_0_45]), c_0_46]), c_0_95]), c_0_96]), c_0_47])]), c_0_38])).
cnf(c_0_107, negated_conjecture, (v1_funct_2(k9_ringder1(esk1_0),u1_struct_0(k12_polynom3(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(spm,[status(thm)],[c_0_97, c_0_43]), c_0_44]), c_0_94]), c_0_45]), c_0_46]), c_0_95]), c_0_96]), c_0_47])]), c_0_38])).
cnf(c_0_108, negated_conjecture, (v1_funct_1(k9_ringder1(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(spm,[status(thm)],[c_0_98, c_0_43]), c_0_44]), c_0_94]), c_0_45]), c_0_46]), c_0_95]), c_0_96]), c_0_47])]), c_0_38])).
cnf(c_0_109, plain, (v1_funct_1(k1_vectsp11(X1,X2,X3))|~l1_struct_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|~v7_ordinal1(X3)), inference(split_conjunct,[status(thm)],[c_0_68])).
fof(c_0_110, plain, ![X71, X72, X73]:(v2_struct_0(X71)|v6_struct_0(X71)|~v13_algstr_0(X71)|~v3_group_1(X71)|~v5_group_1(X71)|~v2_rlvect_1(X71)|~v3_rlvect_1(X71)|~v4_rlvect_1(X71)|~v4_vectsp_1(X71)|~v5_vectsp_1(X71)|~l6_algstr_0(X71)|~v1_funct_1(X72)|~v1_funct_2(X72,u1_struct_0(k12_polynom3(X71)),u1_struct_0(k12_polynom3(X71)))|~m1_subset_1(X72,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(X71)),u1_struct_0(k12_polynom3(X71)))))|~m1_subset_1(X73,u1_struct_0(k12_polynom3(X71)))|k8_ringder1(X71,X72,X73)=k1_funct_1(X72,X73)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_99])])).
fof(c_0_111, plain, ![X53, X54, X55]:(v2_struct_0(X53)|~v1_group_1(X53)|~l3_algstr_0(X53)|~m1_subset_1(X54,u1_struct_0(X53))|~v7_ordinal1(X55)|m1_subset_1(k2_binom(X53,X54,X55),u1_struct_0(X53))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])).
cnf(c_0_112, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(k12_polynom3(esk1_0)))|~l1_struct_0(k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102]), c_0_55])).
cnf(c_0_113, negated_conjecture, (v1_group_1(k12_polynom3(esk1_0))|~v4_vectsp_1(k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_87]), c_0_55])).
cnf(c_0_114, negated_conjecture, (v4_vectsp_1(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(spm,[status(thm)],[c_0_104, c_0_43]), c_0_44]), c_0_94]), c_0_45]), c_0_46]), c_0_47])]), c_0_38])).
cnf(c_0_115, negated_conjecture, (k1_vectsp11(k12_polynom3(esk1_0),k9_ringder1(esk1_0),k5_numbers)=k3_struct_0(k12_polynom3(esk1_0))|~v1_funct_1(k1_vectsp11(k12_polynom3(esk1_0),k9_ringder1(esk1_0),k5_numbers))|~l1_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_106]), c_0_107]), c_0_108])])).
cnf(c_0_116, negated_conjecture, (v1_funct_1(k1_vectsp11(k12_polynom3(esk1_0),k9_ringder1(esk1_0),X1))|~l1_struct_0(k12_polynom3(esk1_0))|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_106]), c_0_107]), c_0_108])])).
cnf(c_0_117, plain, (v2_struct_0(X1)|v6_struct_0(X1)|k8_ringder1(X1,X2,X3)=k1_funct_1(X2,X3)|~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)|~l6_algstr_0(X1)|~v1_funct_1(X2)|~v1_funct_2(X2,u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1)))|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom3(X1)),u1_struct_0(k12_polynom3(X1)))))|~m1_subset_1(X3,u1_struct_0(k12_polynom3(X1)))), inference(split_conjunct,[status(thm)],[c_0_110])).
cnf(c_0_118, 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_111])).
cnf(c_0_119, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(k12_polynom3(esk1_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_86]), c_0_87])])).
cnf(c_0_120, negated_conjecture, (v1_group_1(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113, c_0_114])])).
fof(c_0_121, plain, ![X68, X69]:(~m1_subset_1(X69,X68)|k1_funct_1(k4_relat_1(X68),X69)=X69), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rd1_funct_1])])).
fof(c_0_122, plain, ![X70]:k6_partfun1(X70)=k4_relat_1(X70), inference(variable_rename,[status(thm)],[redefinition_k6_partfun1])).
cnf(c_0_123, negated_conjecture, (k8_ringder1(esk1_0,k1_vectsp11(k12_polynom3(esk1_0),k9_ringder1(esk1_0),k5_numbers),k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0))!=k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_124, negated_conjecture, (k1_vectsp11(k12_polynom3(esk1_0),k9_ringder1(esk1_0),k5_numbers)=k3_struct_0(k12_polynom3(esk1_0))|~l1_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_82])])).
cnf(c_0_125, plain, (k8_ringder1(X1,k3_struct_0(k12_polynom3(X1)),X2)=k1_funct_1(k3_struct_0(k12_polynom3(X1)),X2)|v6_struct_0(X1)|v2_struct_0(X1)|~m1_subset_1(X2,u1_struct_0(k12_polynom3(X1)))|~l1_struct_0(k12_polynom3(X1))|~l6_algstr_0(X1)|~v5_vectsp_1(X1)|~v4_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v2_rlvect_1(X1)|~v5_group_1(X1)|~v3_group_1(X1)|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_57]), c_0_58]), c_0_59])).
cnf(c_0_126, negated_conjecture, (m1_subset_1(k2_binom(k12_polynom3(esk1_0),esk3_0,X1),u1_struct_0(k12_polynom3(esk1_0)))|~l3_algstr_0(k12_polynom3(esk1_0))|~v7_ordinal1(X1)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119]), c_0_120])]), c_0_55])).
cnf(c_0_127, negated_conjecture, (v5_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_128, negated_conjecture, (~v6_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_129, plain, (k1_funct_1(k4_relat_1(X2),X1)=X1|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_121])).
cnf(c_0_130, plain, (k6_partfun1(X1)=k4_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_122])).
fof(c_0_131, plain, ![X48]:(~l1_struct_0(X48)|k3_struct_0(X48)=k6_partfun1(u1_struct_0(X48))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_struct_0])])).
cnf(c_0_132, negated_conjecture, (k8_ringder1(esk1_0,k3_struct_0(k12_polynom3(esk1_0)),k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0))!=k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0)|~l1_struct_0(k12_polynom3(esk1_0))), inference(spm,[status(thm)],[c_0_123, c_0_124])).
cnf(c_0_133, negated_conjecture, (k8_ringder1(esk1_0,k3_struct_0(k12_polynom3(esk1_0)),k2_binom(k12_polynom3(esk1_0),esk3_0,X1))=k1_funct_1(k3_struct_0(k12_polynom3(esk1_0)),k2_binom(k12_polynom3(esk1_0),esk3_0,X1))|~l3_algstr_0(k12_polynom3(esk1_0))|~l1_struct_0(k12_polynom3(esk1_0))|~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(spm,[status(thm)],[c_0_125, c_0_126]), c_0_43]), c_0_44]), c_0_94]), c_0_45]), c_0_46]), c_0_95]), c_0_127]), c_0_96]), c_0_47])]), c_0_128]), c_0_38])).
cnf(c_0_134, negated_conjecture, (v7_ordinal1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_30])).
cnf(c_0_135, plain, (k1_funct_1(k6_partfun1(X2),X1)=X1|~m1_subset_1(X1,X2)), inference(rw,[status(thm)],[c_0_129, c_0_130])).
cnf(c_0_136, plain, (k3_struct_0(X1)=k6_partfun1(u1_struct_0(X1))|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_131])).
cnf(c_0_137, negated_conjecture, (k1_funct_1(k3_struct_0(k12_polynom3(esk1_0)),k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0))!=k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0)|~l3_algstr_0(k12_polynom3(esk1_0))|~l1_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133]), c_0_134])])).
cnf(c_0_138, plain, (k1_funct_1(k3_struct_0(X1),X2)=X2|~m1_subset_1(X2,u1_struct_0(X1))|~l1_struct_0(X1)), inference(spm,[status(thm)],[c_0_135, c_0_136])).
cnf(c_0_139, negated_conjecture, (~l3_algstr_0(k12_polynom3(esk1_0))|~m1_subset_1(k2_binom(k12_polynom3(esk1_0),esk3_0,esk2_0),u1_struct_0(k12_polynom3(esk1_0)))|~l1_struct_0(k12_polynom3(esk1_0))), inference(spm,[status(thm)],[c_0_137, c_0_138])).
fof(c_0_140, plain, ![X60]:((l3_struct_0(X60)|~l4_algstr_0(X60))&(l3_algstr_0(X60)|~l4_algstr_0(X60))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l4_algstr_0])])])).
cnf(c_0_141, negated_conjecture, (~l3_algstr_0(k12_polynom3(esk1_0))|~l1_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_126]), c_0_134])])).
cnf(c_0_142, plain, (l3_algstr_0(X1)|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_140])).
cnf(c_0_143, negated_conjecture, (~l1_struct_0(k12_polynom3(esk1_0))|~l4_algstr_0(k12_polynom3(esk1_0))), inference(spm,[status(thm)],[c_0_141, c_0_142])).
cnf(c_0_144, negated_conjecture, (~l1_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143, c_0_89]), c_0_87])])).
cnf(c_0_145, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_86]), c_0_87])]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 146
# Proof object clause steps            : 87
# Proof object formula steps           : 59
# Proof object conjectures             : 46
# Proof object clause conjectures      : 43
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 46
# Proof object initial formulas used   : 25
# Proof object generating inferences   : 38
# Proof object simplifying inferences  : 108
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 25
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 58
# Removed in clause preprocessing      : 2
# Initial clauses in saturation        : 56
# Processed clauses                    : 2359
# ...of these trivial                  : 0
# ...subsumed                          : 391
# ...remaining for further processing  : 1968
# Other redundant clauses eliminated   : 1
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 614
# Backward-rewritten                   : 3
# Generated clauses                    : 3512
# ...of the previous two non-trivial   : 3511
# Contextual simplify-reflections      : 40
# Paramodulations                      : 3511
# 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  : 1298
#    Positive orientable unit clauses  : 25
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 5
#    Non-unit-clauses                  : 1268
# Current number of unprocessed clauses: 1260
# ...number of literals in the above   : 4533
# Current number of archived formulas  : 0
# Current number of archived clauses   : 670
# Clause-clause subsumption calls (NU) : 1008470
# Rec. Clause-clause subsumption calls : 507551
# Non-unit clause-clause subsumptions  : 1045
# Unit Clause-clause subsumption calls : 189
# 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          : 282267

# -------------------------------------------------
# User time                : 0.476 s
# System time              : 0.000 s
# Total time               : 0.476 s
# Maximum resident set size: 3396 pages
