# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN
# and selection function PSelectComplexExceptUniqMaxHorn.
#
# Preprocessing time       : 0.024 s
# Presaturation interreduction done

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(cc4_algstr_1, axiom, ![X1]:(l2_algstr_0(X1)=>((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))=>((~(v2_struct_0(X1))&v1_algstr_1(X1))&v4_algstr_1(X1)))), file('e_trans1/e_trans1__t11_e_trans1', cc4_algstr_1)).
fof(dt_l6_algstr_0, axiom, ![X1]:(l6_algstr_0(X1)=>(l2_algstr_0(X1)&l5_algstr_0(X1))), file('e_trans1/e_trans1__t11_e_trans1', dt_l6_algstr_0)).
fof(t11_e_trans1, conjecture, ![X1]:((((((((((((~(v2_struct_0(X1))&~(v6_struct_0(X1)))&v13_algstr_0(X1))&v33_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))=>![X2]:((((((((((((~(v2_struct_0(X2))&~(v6_struct_0(X2)))&v13_algstr_0(X2))&v33_algstr_0(X2))&v3_group_1(X2))&v5_group_1(X2))&v2_rlvect_1(X2))&v3_rlvect_1(X2))&v4_rlvect_1(X2))&v4_vectsp_1(X2))&v5_vectsp_1(X2))&l6_algstr_0(X2))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>((m1_c0sp1(X1,X2)&r1_algnum_1(X1,X2,X3))=>v4_ring_1(k3_algnum_1(X1,X2,X3),k12_polynom3(X1)))))), file('e_trans1/e_trans1__t11_e_trans1', t11_e_trans1)).
fof(cc1_vectsp_1, axiom, ![X1]:(l6_algstr_0(X1)=>((~(v2_struct_0(X1))&v5_vectsp_1(X1))=>((~(v2_struct_0(X1))&v1_vectsp_1(X1))&v2_vectsp_1(X1)))), file('e_trans1/e_trans1__t11_e_trans1', cc1_vectsp_1)).
fof(t33_algnum_1, axiom, ![X1]:((((((((((((~(v2_struct_0(X1))&~(v6_struct_0(X1)))&v13_algstr_0(X1))&v33_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))&v5_group_1(X1))&l6_algstr_0(X1))=>![X2]:((((((((((((~(v2_struct_0(X2))&~(v6_struct_0(X2)))&v13_algstr_0(X2))&v33_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))&v5_group_1(X2))&l6_algstr_0(X2))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>~(((m1_c0sp1(X1,X2)&r1_algnum_1(X1,X2,X3))&![X4]:(m1_subset_1(X4,u1_struct_0(k12_polynom3(X1)))=>~(((X4!=k8_polynom3(X1)&k7_ideal_1(k12_polynom3(X1),k1_ring_4(k12_polynom3(X1),X4))=k3_algnum_1(X1,X2,X3))&X4=k3_ring_4(X1,X4))))))))), file('e_trans1/e_trans1__t11_e_trans1', t33_algnum_1)).
fof(cc2_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))&v5_group_1(X1))&l6_algstr_0(X1))=>![X2]:(m1_c0sp1(X2,X1)=>v5_group_1(X2))), file('e_trans1/e_trans1__t11_e_trans1', cc2_field_4)).
fof(cc1_field_4, axiom, ![X1]:((((((((((~(v2_struct_0(X1))&~(v6_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]:(m1_c0sp1(X2,X1)=>~(v6_struct_0(X2)))), file('e_trans1/e_trans1__t11_e_trans1', cc1_field_4)).
fof(cc1_polynom4, axiom, ![X1]:(l6_algstr_0(X1)=>(((((((~(v2_struct_0(X1))&v6_algstr_0(X1))&v33_algstr_0(X1))&v1_vectsp_1(X1))&v4_vectsp_1(X1))&v3_group_1(X1))&v1_algstr_1(X1))=>((((((~(v2_struct_0(X1))&v6_algstr_0(X1))&v1_vectsp_1(X1))&v4_vectsp_1(X1))&v3_group_1(X1))&v1_vectsp_2(X1))&v1_algstr_1(X1)))), file('e_trans1/e_trans1__t11_e_trans1', cc1_polynom4)).
fof(cc1_algstr_1, axiom, ![X1]:(l2_algstr_0(X1)=>((~(v2_struct_0(X1))&v4_algstr_1(X1))=>((((~(v2_struct_0(X1))&v5_algstr_0(X1))&v6_algstr_0(X1))&v2_algstr_1(X1))&v3_algstr_1(X1)))), file('e_trans1/e_trans1__t11_e_trans1', cc1_algstr_1)).
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_trans1/e_trans1__t11_e_trans1', dt_k12_polynom3)).
fof(fc8_ratfunc1, axiom, ![X1]:((((((~(v6_struct_0(X1))&v13_algstr_0(X1))&v5_vectsp_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&~(v6_struct_0(k12_polynom3(X1))))&v36_algstr_0(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc8_ratfunc1)).
fof(t32_algnum_1, axiom, ![X1]:((((((((((((~(v2_struct_0(X1))&~(v6_struct_0(X1)))&v13_algstr_0(X1))&v33_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))&v5_group_1(X1))&l6_algstr_0(X1))=>![X2]:((((((((((((~(v2_struct_0(X2))&~(v6_struct_0(X2)))&v13_algstr_0(X2))&v33_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))&v5_group_1(X2))&l6_algstr_0(X2))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>((m1_c0sp1(X1,X2)&r1_algnum_1(X1,X2,X3))=>v2_ring_1(k3_algnum_1(X1,X2,X3),k12_polynom3(X1)))))), file('e_trans1/e_trans1__t11_e_trans1', t32_algnum_1)).
fof(fc16_polynom3, axiom, ![X1]:(((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(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)))&v5_vectsp_1(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc16_polynom3)).
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_trans1/e_trans1__t11_e_trans1', fc3_ring_4)).
fof(fc11_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)))&v4_rlvect_1(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc11_polynom3)).
fof(fc10_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)))&v3_rlvect_1(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc10_polynom3)).
fof(fc9_polynom3, axiom, ![X1]:(((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(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_rlvect_1(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc9_polynom3)).
fof(fc13_polynom3, axiom, ![X1]:((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&v5_group_1(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&v5_group_1(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc13_polynom3)).
fof(fc14_polynom3, axiom, ![X1]:(((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&v3_group_1(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc14_polynom3)).
fof(fc12_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)))&v13_algstr_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc12_polynom3)).
fof(fc9_ratfunc1, axiom, ![X1]:(((((((~(v7_struct_0(X1))&v13_algstr_0(X1))&v5_vectsp_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v1_vectsp_2(X1))&l6_algstr_0(X1))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&v1_vectsp_2(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc9_ratfunc1)).
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_trans1/e_trans1__t11_e_trans1', redefinition_k1_ring_4)).
fof(d10_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))=>![X2]:(((~(v2_struct_0(X2))&v36_algstr_0(X2))&l6_algstr_0(X2))=>(X2=k12_polynom3(X1)<=>((((![X3]:(r2_tarski(X3,u1_struct_0(X2))<=>(((v1_funct_1(X3)&v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X3,X1))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))))&![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>![X5]:(((v1_funct_1(X5)&v1_funct_2(X5,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>![X6]:(((v1_funct_1(X6)&v1_funct_2(X6,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>((X3=X5&X4=X6)=>k1_algstr_0(X2,X3,X4)=k1_normsp_1(X1,X5,X6)))))))&![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>![X5]:(((v1_funct_1(X5)&v1_funct_2(X5,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>![X6]:(((v1_funct_1(X6)&v1_funct_2(X6,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>((X3=X5&X4=X6)=>k6_algstr_0(X2,X3,X4)=k10_polynom3(X1,X5,X6)))))))&k4_struct_0(X2)=k8_polynom3(X1))&k5_struct_0(X2)=k9_polynom3(X1))))), file('e_trans1/e_trans1__t11_e_trans1', d10_polynom3)).
fof(fc29_ring_2, axiom, ![X1]:((((((((((((~(v2_struct_0(X1))&~(v6_struct_0(X1)))&v13_algstr_0(X1))&v33_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))=>((~(v2_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))&v1_int_3(k12_polynom3(X1)))), file('e_trans1/e_trans1__t11_e_trans1', fc29_ring_2)).
fof(cc7_ring_2, axiom, ![X1]:((((((((((((~(v2_struct_0(X1))&~(v6_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))&v1_vectsp_2(X1))&l6_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>(v4_ring_2(X2,X1)=>v5_ring_2(X2,X1)))), file('e_trans1/e_trans1__t11_e_trans1', cc7_ring_2)).
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_trans1/e_trans1__t11_e_trans1', redefinition_k6_domain_1)).
fof(cc11_ring_2, axiom, ![X1]:(l6_algstr_0(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))&v1_int_3(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))&v8_ideal_1(X1)))), file('e_trans1/e_trans1__t11_e_trans1', cc11_ring_2)).
fof(t24_ring_2, axiom, ![X1]:(((((((((((~(v2_struct_0(X1))&~(v6_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]:((~(v9_struct_0(X2,X1))&m1_subset_1(X2,u1_struct_0(X1)))=>(v4_ring_2(X2,X1)<=>v2_ring_1(k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),X2)),X1)))), file('e_trans1/e_trans1__t11_e_trans1', t24_ring_2)).
fof(t26_ring_2, axiom, ![X1]:(((((((((((((~(v2_struct_0(X1))&~(v6_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))&v8_ideal_1(X1))&v1_vectsp_2(X1))&l6_algstr_0(X1))=>![X2]:((~(v9_struct_0(X2,X1))&m1_subset_1(X2,u1_struct_0(X1)))=>(v4_ring_1(k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),X2)),X1)<=>v5_ring_2(X2,X1)))), file('e_trans1/e_trans1__t11_e_trans1', t26_ring_2)).
fof(d12_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>(v9_struct_0(X2,X1)<=>X2=k4_struct_0(X1)))), file('e_trans1/e_trans1__t11_e_trans1', d12_struct_0)).
fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('e_trans1/e_trans1__t11_e_trans1', dt_l2_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_trans1/e_trans1__t11_e_trans1', fc2_struct_0)).
fof(dt_l2_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>l1_struct_0(X1)), file('e_trans1/e_trans1__t11_e_trans1', dt_l2_struct_0)).
fof(cc3_struct_0, axiom, ![X1]:(l4_struct_0(X1)=>(~(v6_struct_0(X1))=>~(v7_struct_0(X1)))), file('e_trans1/e_trans1__t11_e_trans1', cc3_struct_0)).
fof(dt_l5_algstr_0, axiom, ![X1]:(l5_algstr_0(X1)=>(l4_algstr_0(X1)&l4_struct_0(X1))), file('e_trans1/e_trans1__t11_e_trans1', dt_l5_algstr_0)).
fof(c_0_35, plain, ![X1]:(l2_algstr_0(X1)=>((((~v2_struct_0(X1)&v13_algstr_0(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))=>((~v2_struct_0(X1)&v1_algstr_1(X1))&v4_algstr_1(X1)))), inference(fof_simplification,[status(thm)],[cc4_algstr_1])).
fof(c_0_36, plain, ![X79]:(((~v2_struct_0(X79)|(v2_struct_0(X79)|~v13_algstr_0(X79)|~v3_rlvect_1(X79)|~v4_rlvect_1(X79))|~l2_algstr_0(X79))&(v1_algstr_1(X79)|(v2_struct_0(X79)|~v13_algstr_0(X79)|~v3_rlvect_1(X79)|~v4_rlvect_1(X79))|~l2_algstr_0(X79)))&(v4_algstr_1(X79)|(v2_struct_0(X79)|~v13_algstr_0(X79)|~v3_rlvect_1(X79)|~v4_rlvect_1(X79))|~l2_algstr_0(X79))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])).
fof(c_0_37, plain, ![X98]:((l2_algstr_0(X98)|~l6_algstr_0(X98))&(l5_algstr_0(X98)|~l6_algstr_0(X98))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])).
fof(c_0_38, negated_conjecture, ~(![X1]:((((((((((((~v2_struct_0(X1)&~v6_struct_0(X1))&v13_algstr_0(X1))&v33_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))=>![X2]:((((((((((((~v2_struct_0(X2)&~v6_struct_0(X2))&v13_algstr_0(X2))&v33_algstr_0(X2))&v3_group_1(X2))&v5_group_1(X2))&v2_rlvect_1(X2))&v3_rlvect_1(X2))&v4_rlvect_1(X2))&v4_vectsp_1(X2))&v5_vectsp_1(X2))&l6_algstr_0(X2))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>((m1_c0sp1(X1,X2)&r1_algnum_1(X1,X2,X3))=>v4_ring_1(k3_algnum_1(X1,X2,X3),k12_polynom3(X1))))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t11_e_trans1])])).
fof(c_0_39, plain, ![X1]:(l6_algstr_0(X1)=>((~v2_struct_0(X1)&v5_vectsp_1(X1))=>((~v2_struct_0(X1)&v1_vectsp_1(X1))&v2_vectsp_1(X1)))), inference(fof_simplification,[status(thm)],[cc1_vectsp_1])).
fof(c_0_40, plain, ![X1]:((((((((((((~v2_struct_0(X1)&~v6_struct_0(X1))&v13_algstr_0(X1))&v33_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))&v5_group_1(X1))&l6_algstr_0(X1))=>![X2]:((((((((((((~v2_struct_0(X2)&~v6_struct_0(X2))&v13_algstr_0(X2))&v33_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))&v5_group_1(X2))&l6_algstr_0(X2))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>~(((m1_c0sp1(X1,X2)&r1_algnum_1(X1,X2,X3))&![X4]:(m1_subset_1(X4,u1_struct_0(k12_polynom3(X1)))=>~(((X4!=k8_polynom3(X1)&k7_ideal_1(k12_polynom3(X1),k1_ring_4(k12_polynom3(X1),X4))=k3_algnum_1(X1,X2,X3))&X4=k3_ring_4(X1,X4))))))))), inference(fof_simplification,[status(thm)],[t33_algnum_1])).
fof(c_0_41, 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_c0sp1(X2,X1)=>v5_group_1(X2))), inference(fof_simplification,[status(thm)],[cc2_field_4])).
fof(c_0_42, plain, ![X1]:((((((((((~v2_struct_0(X1)&~v6_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]:(m1_c0sp1(X2,X1)=>~v6_struct_0(X2))), inference(fof_simplification,[status(thm)],[cc1_field_4])).
fof(c_0_43, plain, ![X1]:(l6_algstr_0(X1)=>(((((((~v2_struct_0(X1)&v6_algstr_0(X1))&v33_algstr_0(X1))&v1_vectsp_1(X1))&v4_vectsp_1(X1))&v3_group_1(X1))&v1_algstr_1(X1))=>((((((~v2_struct_0(X1)&v6_algstr_0(X1))&v1_vectsp_1(X1))&v4_vectsp_1(X1))&v3_group_1(X1))&v1_vectsp_2(X1))&v1_algstr_1(X1)))), inference(fof_simplification,[status(thm)],[cc1_polynom4])).
cnf(c_0_44, plain, (v1_algstr_1(X1)|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_36])).
cnf(c_0_45, plain, (l2_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_37])).
fof(c_0_46, negated_conjecture, ((((((((((((~v2_struct_0(esk1_0)&~v6_struct_0(esk1_0))&v13_algstr_0(esk1_0))&v33_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))&l6_algstr_0(esk1_0))&((((((((((((~v2_struct_0(esk2_0)&~v6_struct_0(esk2_0))&v13_algstr_0(esk2_0))&v33_algstr_0(esk2_0))&v3_group_1(esk2_0))&v5_group_1(esk2_0))&v2_rlvect_1(esk2_0))&v3_rlvect_1(esk2_0))&v4_rlvect_1(esk2_0))&v4_vectsp_1(esk2_0))&v5_vectsp_1(esk2_0))&l6_algstr_0(esk2_0))&(m1_subset_1(esk3_0,u1_struct_0(esk2_0))&((m1_c0sp1(esk1_0,esk2_0)&r1_algnum_1(esk1_0,esk2_0,esk3_0))&~v4_ring_1(k3_algnum_1(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])).
fof(c_0_47, plain, ![X75]:(((~v2_struct_0(X75)|(v2_struct_0(X75)|~v5_vectsp_1(X75))|~l6_algstr_0(X75))&(v1_vectsp_1(X75)|(v2_struct_0(X75)|~v5_vectsp_1(X75))|~l6_algstr_0(X75)))&(v2_vectsp_1(X75)|(v2_struct_0(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_39])])])).
fof(c_0_48, plain, ![X1]:(l2_algstr_0(X1)=>((~v2_struct_0(X1)&v4_algstr_1(X1))=>((((~v2_struct_0(X1)&v5_algstr_0(X1))&v6_algstr_0(X1))&v2_algstr_1(X1))&v3_algstr_1(X1)))), inference(fof_simplification,[status(thm)],[cc1_algstr_1])).
cnf(c_0_49, plain, (v4_algstr_1(X1)|v2_struct_0(X1)|~v13_algstr_0(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_36])).
fof(c_0_50, plain, ![X122, X123, X124]:((m1_subset_1(esk8_3(X122,X123,X124),u1_struct_0(k12_polynom3(X122)))|(~m1_c0sp1(X122,X123)|~r1_algnum_1(X122,X123,X124))|~m1_subset_1(X124,u1_struct_0(X123))|(v2_struct_0(X123)|v6_struct_0(X123)|~v13_algstr_0(X123)|~v33_algstr_0(X123)|~v2_rlvect_1(X123)|~v3_rlvect_1(X123)|~v4_rlvect_1(X123)|~v4_vectsp_1(X123)|~v5_vectsp_1(X123)|~v3_group_1(X123)|~v5_group_1(X123)|~l6_algstr_0(X123))|(v2_struct_0(X122)|v6_struct_0(X122)|~v13_algstr_0(X122)|~v33_algstr_0(X122)|~v2_rlvect_1(X122)|~v3_rlvect_1(X122)|~v4_rlvect_1(X122)|~v4_vectsp_1(X122)|~v5_vectsp_1(X122)|~v3_group_1(X122)|~v5_group_1(X122)|~l6_algstr_0(X122)))&(((esk8_3(X122,X123,X124)!=k8_polynom3(X122)|(~m1_c0sp1(X122,X123)|~r1_algnum_1(X122,X123,X124))|~m1_subset_1(X124,u1_struct_0(X123))|(v2_struct_0(X123)|v6_struct_0(X123)|~v13_algstr_0(X123)|~v33_algstr_0(X123)|~v2_rlvect_1(X123)|~v3_rlvect_1(X123)|~v4_rlvect_1(X123)|~v4_vectsp_1(X123)|~v5_vectsp_1(X123)|~v3_group_1(X123)|~v5_group_1(X123)|~l6_algstr_0(X123))|(v2_struct_0(X122)|v6_struct_0(X122)|~v13_algstr_0(X122)|~v33_algstr_0(X122)|~v2_rlvect_1(X122)|~v3_rlvect_1(X122)|~v4_rlvect_1(X122)|~v4_vectsp_1(X122)|~v5_vectsp_1(X122)|~v3_group_1(X122)|~v5_group_1(X122)|~l6_algstr_0(X122)))&(k7_ideal_1(k12_polynom3(X122),k1_ring_4(k12_polynom3(X122),esk8_3(X122,X123,X124)))=k3_algnum_1(X122,X123,X124)|(~m1_c0sp1(X122,X123)|~r1_algnum_1(X122,X123,X124))|~m1_subset_1(X124,u1_struct_0(X123))|(v2_struct_0(X123)|v6_struct_0(X123)|~v13_algstr_0(X123)|~v33_algstr_0(X123)|~v2_rlvect_1(X123)|~v3_rlvect_1(X123)|~v4_rlvect_1(X123)|~v4_vectsp_1(X123)|~v5_vectsp_1(X123)|~v3_group_1(X123)|~v5_group_1(X123)|~l6_algstr_0(X123))|(v2_struct_0(X122)|v6_struct_0(X122)|~v13_algstr_0(X122)|~v33_algstr_0(X122)|~v2_rlvect_1(X122)|~v3_rlvect_1(X122)|~v4_rlvect_1(X122)|~v4_vectsp_1(X122)|~v5_vectsp_1(X122)|~v3_group_1(X122)|~v5_group_1(X122)|~l6_algstr_0(X122))))&(esk8_3(X122,X123,X124)=k3_ring_4(X122,esk8_3(X122,X123,X124))|(~m1_c0sp1(X122,X123)|~r1_algnum_1(X122,X123,X124))|~m1_subset_1(X124,u1_struct_0(X123))|(v2_struct_0(X123)|v6_struct_0(X123)|~v13_algstr_0(X123)|~v33_algstr_0(X123)|~v2_rlvect_1(X123)|~v3_rlvect_1(X123)|~v4_rlvect_1(X123)|~v4_vectsp_1(X123)|~v5_vectsp_1(X123)|~v3_group_1(X123)|~v5_group_1(X123)|~l6_algstr_0(X123))|(v2_struct_0(X122)|v6_struct_0(X122)|~v13_algstr_0(X122)|~v33_algstr_0(X122)|~v2_rlvect_1(X122)|~v3_rlvect_1(X122)|~v4_rlvect_1(X122)|~v4_vectsp_1(X122)|~v5_vectsp_1(X122)|~v3_group_1(X122)|~v5_group_1(X122)|~l6_algstr_0(X122))))), 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_40])])])])])).
fof(c_0_51, plain, ![X76, X77]:(v2_struct_0(X76)|~v13_algstr_0(X76)|~v4_vectsp_1(X76)|~v5_vectsp_1(X76)|~v2_rlvect_1(X76)|~v3_rlvect_1(X76)|~v4_rlvect_1(X76)|~v3_group_1(X76)|~v5_group_1(X76)|~l6_algstr_0(X76)|(~m1_c0sp1(X77,X76)|v5_group_1(X77))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])).
fof(c_0_52, plain, ![X72, X73]:(v2_struct_0(X72)|v6_struct_0(X72)|~v13_algstr_0(X72)|~v4_vectsp_1(X72)|~v5_vectsp_1(X72)|~v2_rlvect_1(X72)|~v3_rlvect_1(X72)|~v4_rlvect_1(X72)|~v3_group_1(X72)|~l6_algstr_0(X72)|(~m1_c0sp1(X73,X72)|~v6_struct_0(X73))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])).
fof(c_0_53, plain, ![X74]:(((((((~v2_struct_0(X74)|(v2_struct_0(X74)|~v6_algstr_0(X74)|~v33_algstr_0(X74)|~v1_vectsp_1(X74)|~v4_vectsp_1(X74)|~v3_group_1(X74)|~v1_algstr_1(X74))|~l6_algstr_0(X74))&(v6_algstr_0(X74)|(v2_struct_0(X74)|~v6_algstr_0(X74)|~v33_algstr_0(X74)|~v1_vectsp_1(X74)|~v4_vectsp_1(X74)|~v3_group_1(X74)|~v1_algstr_1(X74))|~l6_algstr_0(X74)))&(v1_vectsp_1(X74)|(v2_struct_0(X74)|~v6_algstr_0(X74)|~v33_algstr_0(X74)|~v1_vectsp_1(X74)|~v4_vectsp_1(X74)|~v3_group_1(X74)|~v1_algstr_1(X74))|~l6_algstr_0(X74)))&(v4_vectsp_1(X74)|(v2_struct_0(X74)|~v6_algstr_0(X74)|~v33_algstr_0(X74)|~v1_vectsp_1(X74)|~v4_vectsp_1(X74)|~v3_group_1(X74)|~v1_algstr_1(X74))|~l6_algstr_0(X74)))&(v3_group_1(X74)|(v2_struct_0(X74)|~v6_algstr_0(X74)|~v33_algstr_0(X74)|~v1_vectsp_1(X74)|~v4_vectsp_1(X74)|~v3_group_1(X74)|~v1_algstr_1(X74))|~l6_algstr_0(X74)))&(v1_vectsp_2(X74)|(v2_struct_0(X74)|~v6_algstr_0(X74)|~v33_algstr_0(X74)|~v1_vectsp_1(X74)|~v4_vectsp_1(X74)|~v3_group_1(X74)|~v1_algstr_1(X74))|~l6_algstr_0(X74)))&(v1_algstr_1(X74)|(v2_struct_0(X74)|~v6_algstr_0(X74)|~v33_algstr_0(X74)|~v1_vectsp_1(X74)|~v4_vectsp_1(X74)|~v3_group_1(X74)|~v1_algstr_1(X74))|~l6_algstr_0(X74))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])).
cnf(c_0_54, plain, (v1_algstr_1(X1)|v2_struct_0(X1)|~l6_algstr_0(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v13_algstr_0(X1)), inference(spm,[status(thm)],[c_0_44, c_0_45])).
cnf(c_0_55, negated_conjecture, (l6_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_56, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_57, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_58, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_59, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_60, plain, (v1_vectsp_1(X1)|v2_struct_0(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_47])).
cnf(c_0_61, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
fof(c_0_62, plain, ![X71]:(((((~v2_struct_0(X71)|(v2_struct_0(X71)|~v4_algstr_1(X71))|~l2_algstr_0(X71))&(v5_algstr_0(X71)|(v2_struct_0(X71)|~v4_algstr_1(X71))|~l2_algstr_0(X71)))&(v6_algstr_0(X71)|(v2_struct_0(X71)|~v4_algstr_1(X71))|~l2_algstr_0(X71)))&(v2_algstr_1(X71)|(v2_struct_0(X71)|~v4_algstr_1(X71))|~l2_algstr_0(X71)))&(v3_algstr_1(X71)|(v2_struct_0(X71)|~v4_algstr_1(X71))|~l2_algstr_0(X71))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])).
cnf(c_0_63, plain, (v4_algstr_1(X1)|v2_struct_0(X1)|~l6_algstr_0(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v13_algstr_0(X1)), inference(spm,[status(thm)],[c_0_49, c_0_45])).
cnf(c_0_64, plain, (m1_subset_1(esk8_3(X1,X2,X3),u1_struct_0(k12_polynom3(X1)))|v2_struct_0(X2)|v6_struct_0(X2)|v2_struct_0(X1)|v6_struct_0(X1)|~m1_c0sp1(X1,X2)|~r1_algnum_1(X1,X2,X3)|~m1_subset_1(X3,u1_struct_0(X2))|~v13_algstr_0(X2)|~v33_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)|~v5_group_1(X2)|~l6_algstr_0(X2)|~v13_algstr_0(X1)|~v33_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)|~v5_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_65, plain, (v2_struct_0(X1)|v5_group_1(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)|~v5_group_1(X1)|~l6_algstr_0(X1)|~m1_c0sp1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_51])).
cnf(c_0_66, plain, (v2_struct_0(X1)|v6_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)|~m1_c0sp1(X2,X1)|~v6_struct_0(X2)), inference(split_conjunct,[status(thm)],[c_0_52])).
fof(c_0_67, 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_68, plain, ![X1]:((((((~v6_struct_0(X1)&v13_algstr_0(X1))&v5_vectsp_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&~v6_struct_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc8_ratfunc1])).
fof(c_0_69, plain, ![X1]:((((((((((((~v2_struct_0(X1)&~v6_struct_0(X1))&v13_algstr_0(X1))&v33_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))&v5_group_1(X1))&l6_algstr_0(X1))=>![X2]:((((((((((((~v2_struct_0(X2)&~v6_struct_0(X2))&v13_algstr_0(X2))&v33_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))&v5_group_1(X2))&l6_algstr_0(X2))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>((m1_c0sp1(X1,X2)&r1_algnum_1(X1,X2,X3))=>v2_ring_1(k3_algnum_1(X1,X2,X3),k12_polynom3(X1)))))), inference(fof_simplification,[status(thm)],[t32_algnum_1])).
fof(c_0_70, plain, ![X2, X1]:(epred1_2(X1,X2)<=>(![X3]:(r2_tarski(X3,u1_struct_0(X2))<=>(((v1_funct_1(X3)&v1_funct_2(X3,k4_ordinal1,u1_struct_0(X1)))&v1_polynom1(X3,X1))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1))))))&![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>![X5]:(((v1_funct_1(X5)&v1_funct_2(X5,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>![X6]:(((v1_funct_1(X6)&v1_funct_2(X6,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>((X3=X5&X4=X6)=>k1_algstr_0(X2,X3,X4)=k1_normsp_1(X1,X5,X6)))))))), introduced(definition)).
fof(c_0_71, plain, ![X1]:(((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(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)))&v5_vectsp_1(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc16_polynom3])).
fof(c_0_72, 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])).
fof(c_0_73, 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)))&v4_rlvect_1(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc11_polynom3])).
fof(c_0_74, 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)))&v3_rlvect_1(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc10_polynom3])).
fof(c_0_75, plain, ![X1]:(((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(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_rlvect_1(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc9_polynom3])).
fof(c_0_76, plain, ![X1]:((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v5_vectsp_1(X1))&v5_group_1(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&v5_group_1(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc13_polynom3])).
fof(c_0_77, plain, ![X1]:(((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&v3_group_1(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc14_polynom3])).
fof(c_0_78, 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))&v13_algstr_0(k12_polynom3(X1)))&v36_algstr_0(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc12_polynom3])).
fof(c_0_79, plain, ![X1]:(((((((~v7_struct_0(X1)&v13_algstr_0(X1))&v5_vectsp_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v1_vectsp_2(X1))&l6_algstr_0(X1))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&v1_vectsp_2(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc9_ratfunc1])).
cnf(c_0_80, plain, (v1_vectsp_2(X1)|v2_struct_0(X1)|~v6_algstr_0(X1)|~v33_algstr_0(X1)|~v1_vectsp_1(X1)|~v4_vectsp_1(X1)|~v3_group_1(X1)|~v1_algstr_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_53])).
cnf(c_0_81, negated_conjecture, (v1_algstr_1(esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_56]), c_0_57]), c_0_58])]), c_0_59])).
cnf(c_0_82, negated_conjecture, (v1_vectsp_1(esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_55]), c_0_61])]), c_0_59])).
cnf(c_0_83, negated_conjecture, (v4_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_84, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_85, negated_conjecture, (v33_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_86, plain, (v6_algstr_0(X1)|v2_struct_0(X1)|~v4_algstr_1(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_62])).
cnf(c_0_87, negated_conjecture, (v4_algstr_1(esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_55]), c_0_56]), c_0_57]), c_0_58])]), c_0_59])).
fof(c_0_88, 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])).
cnf(c_0_89, plain, (m1_subset_1(esk8_3(X1,X2,X3),u1_struct_0(k12_polynom3(X1)))|v6_struct_0(X2)|v2_struct_0(X1)|v2_struct_0(X2)|~r1_algnum_1(X1,X2,X3)|~m1_c0sp1(X1,X2)|~m1_subset_1(X3,u1_struct_0(X2))|~l6_algstr_0(X2)|~l6_algstr_0(X1)|~v5_vectsp_1(X2)|~v5_vectsp_1(X1)|~v4_vectsp_1(X2)|~v4_vectsp_1(X1)|~v4_rlvect_1(X2)|~v4_rlvect_1(X1)|~v3_rlvect_1(X2)|~v3_rlvect_1(X1)|~v2_rlvect_1(X2)|~v2_rlvect_1(X1)|~v5_group_1(X2)|~v3_group_1(X2)|~v3_group_1(X1)|~v33_algstr_0(X2)|~v33_algstr_0(X1)|~v13_algstr_0(X2)|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_64, c_0_65]), c_0_66])).
cnf(c_0_90, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_91, negated_conjecture, (l6_algstr_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_92, negated_conjecture, (v5_vectsp_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_93, negated_conjecture, (v4_vectsp_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_94, negated_conjecture, (v4_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_95, negated_conjecture, (v3_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_96, negated_conjecture, (v2_rlvect_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_97, negated_conjecture, (v5_group_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_98, negated_conjecture, (v3_group_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_99, negated_conjecture, (v33_algstr_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_100, negated_conjecture, (v13_algstr_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_101, negated_conjecture, (~v6_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_102, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
fof(c_0_103, plain, ![X94]:(((~v2_struct_0(k12_polynom3(X94))|(v2_struct_0(X94)|~v13_algstr_0(X94)|~v3_rlvect_1(X94)|~v4_rlvect_1(X94)|~v5_vectsp_1(X94)|~l6_algstr_0(X94)))&(v36_algstr_0(k12_polynom3(X94))|(v2_struct_0(X94)|~v13_algstr_0(X94)|~v3_rlvect_1(X94)|~v4_rlvect_1(X94)|~v5_vectsp_1(X94)|~l6_algstr_0(X94))))&(l6_algstr_0(k12_polynom3(X94))|(v2_struct_0(X94)|~v13_algstr_0(X94)|~v3_rlvect_1(X94)|~v4_rlvect_1(X94)|~v5_vectsp_1(X94)|~l6_algstr_0(X94)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])])).
fof(c_0_104, plain, ![X108]:(((~v2_struct_0(k12_polynom3(X108))|(v6_struct_0(X108)|~v13_algstr_0(X108)|~v5_vectsp_1(X108)|~v3_rlvect_1(X108)|~v4_rlvect_1(X108)|~l6_algstr_0(X108)))&(~v6_struct_0(k12_polynom3(X108))|(v6_struct_0(X108)|~v13_algstr_0(X108)|~v5_vectsp_1(X108)|~v3_rlvect_1(X108)|~v4_rlvect_1(X108)|~l6_algstr_0(X108))))&(v36_algstr_0(k12_polynom3(X108))|(v6_struct_0(X108)|~v13_algstr_0(X108)|~v5_vectsp_1(X108)|~v3_rlvect_1(X108)|~v4_rlvect_1(X108)|~l6_algstr_0(X108)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])).
fof(c_0_105, plain, ![X119, X120, X121]:(v2_struct_0(X119)|v6_struct_0(X119)|~v13_algstr_0(X119)|~v33_algstr_0(X119)|~v2_rlvect_1(X119)|~v3_rlvect_1(X119)|~v4_rlvect_1(X119)|~v4_vectsp_1(X119)|~v5_vectsp_1(X119)|~v3_group_1(X119)|~v5_group_1(X119)|~l6_algstr_0(X119)|(v2_struct_0(X120)|v6_struct_0(X120)|~v13_algstr_0(X120)|~v33_algstr_0(X120)|~v2_rlvect_1(X120)|~v3_rlvect_1(X120)|~v4_rlvect_1(X120)|~v4_vectsp_1(X120)|~v5_vectsp_1(X120)|~v3_group_1(X120)|~v5_group_1(X120)|~l6_algstr_0(X120)|(~m1_subset_1(X121,u1_struct_0(X120))|(~m1_c0sp1(X119,X120)|~r1_algnum_1(X119,X120,X121)|v2_ring_1(k3_algnum_1(X119,X120,X121),k12_polynom3(X119)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])).
fof(c_0_106, 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))=>![X2]:(((~v2_struct_0(X2)&v36_algstr_0(X2))&l6_algstr_0(X2))=>(X2=k12_polynom3(X1)<=>(((epred1_2(X1,X2)&![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>![X5]:(((v1_funct_1(X5)&v1_funct_2(X5,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>![X6]:(((v1_funct_1(X6)&v1_funct_2(X6,k4_ordinal1,u1_struct_0(X1)))&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X1)))))=>((X3=X5&X4=X6)=>k6_algstr_0(X2,X3,X4)=k10_polynom3(X1,X5,X6)))))))&k4_struct_0(X2)=k8_polynom3(X1))&k5_struct_0(X2)=k9_polynom3(X1))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[d10_polynom3]), c_0_70])).
fof(c_0_107, plain, ![X1]:((((((((((((~v2_struct_0(X1)&~v6_struct_0(X1))&v13_algstr_0(X1))&v33_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))=>((~v2_struct_0(k12_polynom3(X1))&v36_algstr_0(k12_polynom3(X1)))&v1_int_3(k12_polynom3(X1)))), inference(fof_simplification,[status(thm)],[fc29_ring_2])).
fof(c_0_108, plain, ![X1]:((((((((((((~v2_struct_0(X1)&~v6_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))&v1_vectsp_2(X1))&l6_algstr_0(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>(v4_ring_2(X2,X1)=>v5_ring_2(X2,X1)))), inference(fof_simplification,[status(thm)],[cc7_ring_2])).
fof(c_0_109, plain, ![X104]:(((~v2_struct_0(k12_polynom3(X104))|(v2_struct_0(X104)|~v13_algstr_0(X104)|~v2_rlvect_1(X104)|~v3_rlvect_1(X104)|~v4_rlvect_1(X104)|~v5_vectsp_1(X104)|~l6_algstr_0(X104)))&(v36_algstr_0(k12_polynom3(X104))|(v2_struct_0(X104)|~v13_algstr_0(X104)|~v2_rlvect_1(X104)|~v3_rlvect_1(X104)|~v4_rlvect_1(X104)|~v5_vectsp_1(X104)|~l6_algstr_0(X104))))&(v5_vectsp_1(k12_polynom3(X104))|(v2_struct_0(X104)|~v13_algstr_0(X104)|~v2_rlvect_1(X104)|~v3_rlvect_1(X104)|~v4_rlvect_1(X104)|~v5_vectsp_1(X104)|~l6_algstr_0(X104)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])).
fof(c_0_110, plain, ![X107]:(((~v2_struct_0(k12_polynom3(X107))|(v2_struct_0(X107)|~v13_algstr_0(X107)|~v3_rlvect_1(X107)|~v4_rlvect_1(X107)|~v4_vectsp_1(X107)|~v5_vectsp_1(X107)|~l6_algstr_0(X107)))&(v36_algstr_0(k12_polynom3(X107))|(v2_struct_0(X107)|~v13_algstr_0(X107)|~v3_rlvect_1(X107)|~v4_rlvect_1(X107)|~v4_vectsp_1(X107)|~v5_vectsp_1(X107)|~l6_algstr_0(X107))))&(v4_vectsp_1(k12_polynom3(X107))|(v2_struct_0(X107)|~v13_algstr_0(X107)|~v3_rlvect_1(X107)|~v4_rlvect_1(X107)|~v4_vectsp_1(X107)|~v5_vectsp_1(X107)|~l6_algstr_0(X107)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])).
fof(c_0_111, plain, ![X100]:(((~v2_struct_0(k12_polynom3(X100))|(v2_struct_0(X100)|~v13_algstr_0(X100)|~v3_rlvect_1(X100)|~v4_rlvect_1(X100)|~v5_vectsp_1(X100)|~l6_algstr_0(X100)))&(v36_algstr_0(k12_polynom3(X100))|(v2_struct_0(X100)|~v13_algstr_0(X100)|~v3_rlvect_1(X100)|~v4_rlvect_1(X100)|~v5_vectsp_1(X100)|~l6_algstr_0(X100))))&(v4_rlvect_1(k12_polynom3(X100))|(v2_struct_0(X100)|~v13_algstr_0(X100)|~v3_rlvect_1(X100)|~v4_rlvect_1(X100)|~v5_vectsp_1(X100)|~l6_algstr_0(X100)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_73])])])).
fof(c_0_112, plain, ![X99]:(((~v2_struct_0(k12_polynom3(X99))|(v2_struct_0(X99)|~v13_algstr_0(X99)|~v3_rlvect_1(X99)|~v4_rlvect_1(X99)|~v5_vectsp_1(X99)|~l6_algstr_0(X99)))&(v36_algstr_0(k12_polynom3(X99))|(v2_struct_0(X99)|~v13_algstr_0(X99)|~v3_rlvect_1(X99)|~v4_rlvect_1(X99)|~v5_vectsp_1(X99)|~l6_algstr_0(X99))))&(v3_rlvect_1(k12_polynom3(X99))|(v2_struct_0(X99)|~v13_algstr_0(X99)|~v3_rlvect_1(X99)|~v4_rlvect_1(X99)|~v5_vectsp_1(X99)|~l6_algstr_0(X99)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])).
fof(c_0_113, plain, ![X109]:(((~v2_struct_0(k12_polynom3(X109))|(v2_struct_0(X109)|~v13_algstr_0(X109)|~v2_rlvect_1(X109)|~v3_rlvect_1(X109)|~v4_rlvect_1(X109)|~v5_vectsp_1(X109)|~l6_algstr_0(X109)))&(v36_algstr_0(k12_polynom3(X109))|(v2_struct_0(X109)|~v13_algstr_0(X109)|~v2_rlvect_1(X109)|~v3_rlvect_1(X109)|~v4_rlvect_1(X109)|~v5_vectsp_1(X109)|~l6_algstr_0(X109))))&(v2_rlvect_1(k12_polynom3(X109))|(v2_struct_0(X109)|~v13_algstr_0(X109)|~v2_rlvect_1(X109)|~v3_rlvect_1(X109)|~v4_rlvect_1(X109)|~v5_vectsp_1(X109)|~l6_algstr_0(X109)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])).
fof(c_0_114, plain, ![X102]:(((~v2_struct_0(k12_polynom3(X102))|(v2_struct_0(X102)|~v13_algstr_0(X102)|~v2_rlvect_1(X102)|~v3_rlvect_1(X102)|~v4_rlvect_1(X102)|~v5_vectsp_1(X102)|~v5_group_1(X102)|~l6_algstr_0(X102)))&(v36_algstr_0(k12_polynom3(X102))|(v2_struct_0(X102)|~v13_algstr_0(X102)|~v2_rlvect_1(X102)|~v3_rlvect_1(X102)|~v4_rlvect_1(X102)|~v5_vectsp_1(X102)|~v5_group_1(X102)|~l6_algstr_0(X102))))&(v5_group_1(k12_polynom3(X102))|(v2_struct_0(X102)|~v13_algstr_0(X102)|~v2_rlvect_1(X102)|~v3_rlvect_1(X102)|~v4_rlvect_1(X102)|~v5_vectsp_1(X102)|~v5_group_1(X102)|~l6_algstr_0(X102)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])])).
fof(c_0_115, plain, ![X103]:(((~v2_struct_0(k12_polynom3(X103))|(v2_struct_0(X103)|~v13_algstr_0(X103)|~v2_rlvect_1(X103)|~v3_rlvect_1(X103)|~v4_rlvect_1(X103)|~v4_vectsp_1(X103)|~v5_vectsp_1(X103)|~v3_group_1(X103)|~l6_algstr_0(X103)))&(v36_algstr_0(k12_polynom3(X103))|(v2_struct_0(X103)|~v13_algstr_0(X103)|~v2_rlvect_1(X103)|~v3_rlvect_1(X103)|~v4_rlvect_1(X103)|~v4_vectsp_1(X103)|~v5_vectsp_1(X103)|~v3_group_1(X103)|~l6_algstr_0(X103))))&(v3_group_1(k12_polynom3(X103))|(v2_struct_0(X103)|~v13_algstr_0(X103)|~v2_rlvect_1(X103)|~v3_rlvect_1(X103)|~v4_rlvect_1(X103)|~v4_vectsp_1(X103)|~v5_vectsp_1(X103)|~v3_group_1(X103)|~l6_algstr_0(X103)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])])).
fof(c_0_116, plain, ![X101]:(((~v2_struct_0(k12_polynom3(X101))|(v2_struct_0(X101)|~v13_algstr_0(X101)|~v3_rlvect_1(X101)|~v4_rlvect_1(X101)|~v5_vectsp_1(X101)|~l6_algstr_0(X101)))&(v13_algstr_0(k12_polynom3(X101))|(v2_struct_0(X101)|~v13_algstr_0(X101)|~v3_rlvect_1(X101)|~v4_rlvect_1(X101)|~v5_vectsp_1(X101)|~l6_algstr_0(X101))))&(v36_algstr_0(k12_polynom3(X101))|(v2_struct_0(X101)|~v13_algstr_0(X101)|~v3_rlvect_1(X101)|~v4_rlvect_1(X101)|~v5_vectsp_1(X101)|~l6_algstr_0(X101)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])])).
fof(c_0_117, plain, ![X110]:(((~v2_struct_0(k12_polynom3(X110))|(v7_struct_0(X110)|~v13_algstr_0(X110)|~v5_vectsp_1(X110)|~v3_rlvect_1(X110)|~v4_rlvect_1(X110)|~v1_vectsp_2(X110)|~l6_algstr_0(X110)))&(v36_algstr_0(k12_polynom3(X110))|(v7_struct_0(X110)|~v13_algstr_0(X110)|~v5_vectsp_1(X110)|~v3_rlvect_1(X110)|~v4_rlvect_1(X110)|~v1_vectsp_2(X110)|~l6_algstr_0(X110))))&(v1_vectsp_2(k12_polynom3(X110))|(v7_struct_0(X110)|~v13_algstr_0(X110)|~v5_vectsp_1(X110)|~v3_rlvect_1(X110)|~v4_rlvect_1(X110)|~v1_vectsp_2(X110)|~l6_algstr_0(X110)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])])).
cnf(c_0_118, negated_conjecture, (v1_vectsp_2(esk1_0)|~v6_algstr_0(esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_81]), c_0_82]), c_0_55]), c_0_83]), c_0_84]), c_0_85])]), c_0_59])).
cnf(c_0_119, negated_conjecture, (v6_algstr_0(esk1_0)|~l2_algstr_0(esk1_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_59])).
fof(c_0_120, 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_121, plain, ![X111, X112]:(v2_struct_0(X111)|~l6_algstr_0(X111)|~m1_subset_1(X112,u1_struct_0(X111))|k1_ring_4(X111,X112)=k1_tarski(X112)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])).
cnf(c_0_122, negated_conjecture, (m1_subset_1(esk8_3(X1,esk2_0,esk3_0),u1_struct_0(k12_polynom3(X1)))|v2_struct_0(X1)|~r1_algnum_1(X1,esk2_0,esk3_0)|~m1_c0sp1(X1,esk2_0)|~l6_algstr_0(X1)|~v5_vectsp_1(X1)|~v4_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v2_rlvect_1(X1)|~v3_group_1(X1)|~v33_algstr_0(X1)|~v13_algstr_0(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(spm,[status(thm)],[c_0_89, c_0_90]), c_0_91]), c_0_92]), c_0_93]), c_0_94]), c_0_95]), c_0_96]), c_0_97]), c_0_98]), c_0_99]), c_0_100])]), c_0_101]), c_0_102])).
cnf(c_0_123, negated_conjecture, (r1_algnum_1(esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_124, negated_conjecture, (m1_c0sp1(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_125, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_126, 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_103])).
cnf(c_0_127, negated_conjecture, (~v6_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_128, plain, (v6_struct_0(X1)|~v2_struct_0(k12_polynom3(X1))|~v13_algstr_0(X1)|~v5_vectsp_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_104])).
cnf(c_0_129, plain, (v2_struct_0(X1)|v6_struct_0(X1)|v2_struct_0(X2)|v6_struct_0(X2)|v2_ring_1(k3_algnum_1(X1,X2,X3),k12_polynom3(X1))|~v13_algstr_0(X1)|~v33_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)|~v5_group_1(X1)|~l6_algstr_0(X1)|~v13_algstr_0(X2)|~v33_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)|~v5_group_1(X2)|~l6_algstr_0(X2)|~m1_subset_1(X3,u1_struct_0(X2))|~m1_c0sp1(X1,X2)|~r1_algnum_1(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_105])).
fof(c_0_130, plain, ![X82, X83, X84, X85, X86, X87]:(((((epred1_2(X82,X83)|X83!=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82)))&(~m1_subset_1(X84,u1_struct_0(X83))|(~m1_subset_1(X85,u1_struct_0(X83))|(~v1_funct_1(X86)|~v1_funct_2(X86,k4_ordinal1,u1_struct_0(X82))|~m1_subset_1(X86,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X82))))|(~v1_funct_1(X87)|~v1_funct_2(X87,k4_ordinal1,u1_struct_0(X82))|~m1_subset_1(X87,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X82))))|(X84!=X86|X85!=X87|k6_algstr_0(X83,X84,X85)=k10_polynom3(X82,X86,X87)))))|X83!=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))&(k4_struct_0(X83)=k8_polynom3(X82)|X83!=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))&(k5_struct_0(X83)=k9_polynom3(X82)|X83!=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))&((m1_subset_1(esk4_2(X82,X83),u1_struct_0(X83))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82)))&((m1_subset_1(esk5_2(X82,X83),u1_struct_0(X83))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82)))&((((v1_funct_1(esk6_2(X82,X83))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82)))&(v1_funct_2(esk6_2(X82,X83),k4_ordinal1,u1_struct_0(X82))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))&(m1_subset_1(esk6_2(X82,X83),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X82))))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))&((((v1_funct_1(esk7_2(X82,X83))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82)))&(v1_funct_2(esk7_2(X82,X83),k4_ordinal1,u1_struct_0(X82))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))&(m1_subset_1(esk7_2(X82,X83),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(X82))))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))&(((esk4_2(X82,X83)=esk6_2(X82,X83)|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82)))&(esk5_2(X82,X83)=esk7_2(X82,X83)|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))&(k6_algstr_0(X83,esk4_2(X82,X83),esk5_2(X82,X83))!=k10_polynom3(X82,esk6_2(X82,X83),esk7_2(X82,X83))|~epred1_2(X82,X83)|k4_struct_0(X83)!=k8_polynom3(X82)|k5_struct_0(X83)!=k9_polynom3(X82)|X83=k12_polynom3(X82)|(v2_struct_0(X83)|~v36_algstr_0(X83)|~l6_algstr_0(X83))|(v2_struct_0(X82)|~v13_algstr_0(X82)|~v3_rlvect_1(X82)|~v4_rlvect_1(X82)|~v5_vectsp_1(X82)|~l6_algstr_0(X82))))))))), 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_106])])])])])).
fof(c_0_131, plain, ![X1]:(l6_algstr_0(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))&v1_int_3(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))&v8_ideal_1(X1)))), inference(fof_simplification,[status(thm)],[cc11_ring_2])).
fof(c_0_132, plain, ![X105]:(((~v2_struct_0(k12_polynom3(X105))|(v2_struct_0(X105)|v6_struct_0(X105)|~v13_algstr_0(X105)|~v33_algstr_0(X105)|~v4_vectsp_1(X105)|~v5_vectsp_1(X105)|~v2_rlvect_1(X105)|~v3_rlvect_1(X105)|~v4_rlvect_1(X105)|~v3_group_1(X105)|~v5_group_1(X105)|~l6_algstr_0(X105)))&(v36_algstr_0(k12_polynom3(X105))|(v2_struct_0(X105)|v6_struct_0(X105)|~v13_algstr_0(X105)|~v33_algstr_0(X105)|~v4_vectsp_1(X105)|~v5_vectsp_1(X105)|~v2_rlvect_1(X105)|~v3_rlvect_1(X105)|~v4_rlvect_1(X105)|~v3_group_1(X105)|~v5_group_1(X105)|~l6_algstr_0(X105))))&(v1_int_3(k12_polynom3(X105))|(v2_struct_0(X105)|v6_struct_0(X105)|~v13_algstr_0(X105)|~v33_algstr_0(X105)|~v4_vectsp_1(X105)|~v5_vectsp_1(X105)|~v2_rlvect_1(X105)|~v3_rlvect_1(X105)|~v4_rlvect_1(X105)|~v3_group_1(X105)|~v5_group_1(X105)|~l6_algstr_0(X105)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])])).
fof(c_0_133, plain, ![X80, X81]:(v2_struct_0(X80)|v6_struct_0(X80)|~v13_algstr_0(X80)|~v4_vectsp_1(X80)|~v5_vectsp_1(X80)|~v2_rlvect_1(X80)|~v3_rlvect_1(X80)|~v4_rlvect_1(X80)|~v3_group_1(X80)|~v5_group_1(X80)|~v1_vectsp_2(X80)|~l6_algstr_0(X80)|(~m1_subset_1(X81,u1_struct_0(X80))|(~v4_ring_2(X81,X80)|v5_ring_2(X81,X80)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])])])).
cnf(c_0_134, plain, (v5_vectsp_1(k12_polynom3(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_109])).
cnf(c_0_135, 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_110])).
cnf(c_0_136, plain, (v4_rlvect_1(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_111])).
cnf(c_0_137, plain, (v3_rlvect_1(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_112])).
cnf(c_0_138, plain, (v2_rlvect_1(k12_polynom3(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_113])).
cnf(c_0_139, plain, (v5_group_1(k12_polynom3(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v5_vectsp_1(X1)|~v5_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_114])).
cnf(c_0_140, negated_conjecture, (v5_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_141, plain, (v3_group_1(k12_polynom3(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_115])).
cnf(c_0_142, plain, (v13_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_116])).
cnf(c_0_143, plain, (v1_vectsp_2(k12_polynom3(X1))|v7_struct_0(X1)|~v13_algstr_0(X1)|~v5_vectsp_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v1_vectsp_2(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_117])).
cnf(c_0_144, negated_conjecture, (v1_vectsp_2(esk1_0)|~l2_algstr_0(esk1_0)), inference(spm,[status(thm)],[c_0_118, c_0_119])).
fof(c_0_145, plain, ![X1]:(((((((((((~v2_struct_0(X1)&~v6_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]:((~v9_struct_0(X2,X1)&m1_subset_1(X2,u1_struct_0(X1)))=>(v4_ring_2(X2,X1)<=>v2_ring_1(k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),X2)),X1)))), inference(fof_simplification,[status(thm)],[t24_ring_2])).
fof(c_0_146, plain, ![X113, X114]:(v1_xboole_0(X113)|~m1_subset_1(X114,X113)|k6_domain_1(X113,X114)=k1_tarski(X114)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])])).
cnf(c_0_147, plain, (k7_ideal_1(k12_polynom3(X1),k1_ring_4(k12_polynom3(X1),esk8_3(X1,X2,X3)))=k3_algnum_1(X1,X2,X3)|v2_struct_0(X2)|v6_struct_0(X2)|v2_struct_0(X1)|v6_struct_0(X1)|~m1_c0sp1(X1,X2)|~r1_algnum_1(X1,X2,X3)|~m1_subset_1(X3,u1_struct_0(X2))|~v13_algstr_0(X2)|~v33_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)|~v5_group_1(X2)|~l6_algstr_0(X2)|~v13_algstr_0(X1)|~v33_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)|~v5_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_148, 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_121])).
cnf(c_0_149, negated_conjecture, (m1_subset_1(esk8_3(esk1_0,esk2_0,esk3_0),u1_struct_0(k12_polynom3(esk1_0)))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123]), c_0_124]), c_0_55]), c_0_61]), c_0_83]), c_0_56]), c_0_57]), c_0_125]), c_0_84]), c_0_85]), c_0_58])]), c_0_59])).
cnf(c_0_150, 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_126, c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_58])]), c_0_59])).
cnf(c_0_151, negated_conjecture, (~v2_struct_0(k12_polynom3(esk1_0))), 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_127, c_0_128]), c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_58])])).
cnf(c_0_152, plain, (v2_ring_1(k3_algnum_1(X1,X2,X3),k12_polynom3(X1))|v6_struct_0(X2)|v2_struct_0(X1)|v2_struct_0(X2)|~r1_algnum_1(X1,X2,X3)|~m1_c0sp1(X1,X2)|~m1_subset_1(X3,u1_struct_0(X2))|~l6_algstr_0(X2)|~l6_algstr_0(X1)|~v5_vectsp_1(X2)|~v5_vectsp_1(X1)|~v4_vectsp_1(X2)|~v4_vectsp_1(X1)|~v4_rlvect_1(X2)|~v4_rlvect_1(X1)|~v3_rlvect_1(X2)|~v3_rlvect_1(X1)|~v2_rlvect_1(X2)|~v2_rlvect_1(X1)|~v5_group_1(X2)|~v3_group_1(X2)|~v3_group_1(X1)|~v33_algstr_0(X2)|~v33_algstr_0(X1)|~v13_algstr_0(X2)|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_129, c_0_65]), c_0_66])).
cnf(c_0_153, plain, (k4_struct_0(X1)=k8_polynom3(X2)|v2_struct_0(X1)|v2_struct_0(X2)|X1!=k12_polynom3(X2)|~v36_algstr_0(X1)|~l6_algstr_0(X1)|~v13_algstr_0(X2)|~v3_rlvect_1(X2)|~v4_rlvect_1(X2)|~v5_vectsp_1(X2)|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_130])).
cnf(c_0_154, plain, (v36_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_103])).
cnf(c_0_155, 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_103])).
fof(c_0_156, plain, ![X1]:(((((((((((((~v2_struct_0(X1)&~v6_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))&v8_ideal_1(X1))&v1_vectsp_2(X1))&l6_algstr_0(X1))=>![X2]:((~v9_struct_0(X2,X1)&m1_subset_1(X2,u1_struct_0(X1)))=>(v4_ring_1(k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),X2)),X1)<=>v5_ring_2(X2,X1)))), inference(fof_simplification,[status(thm)],[t26_ring_2])).
fof(c_0_157, plain, ![X70]:((((((((((~v2_struct_0(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70))&(v13_algstr_0(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70)))&(v4_vectsp_1(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70)))&(v5_vectsp_1(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70)))&(v2_rlvect_1(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70)))&(v3_rlvect_1(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70)))&(v4_rlvect_1(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70)))&(v3_group_1(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70)))&(v5_group_1(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70)))&(v8_ideal_1(X70)|(v2_struct_0(X70)|~v13_algstr_0(X70)|~v4_vectsp_1(X70)|~v5_vectsp_1(X70)|~v2_rlvect_1(X70)|~v3_rlvect_1(X70)|~v4_rlvect_1(X70)|~v3_group_1(X70)|~v5_group_1(X70)|~v1_int_3(X70))|~l6_algstr_0(X70))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])])).
cnf(c_0_158, plain, (v1_int_3(k12_polynom3(X1))|v2_struct_0(X1)|v6_struct_0(X1)|~v13_algstr_0(X1)|~v33_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_132])).
cnf(c_0_159, plain, (v2_struct_0(X1)|v6_struct_0(X1)|v5_ring_2(X2,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)|~v1_vectsp_2(X1)|~l6_algstr_0(X1)|~m1_subset_1(X2,u1_struct_0(X1))|~v4_ring_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_133])).
cnf(c_0_160, negated_conjecture, (v5_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_134, c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_125]), c_0_58])]), c_0_59])).
cnf(c_0_161, 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_135, c_0_55]), c_0_61]), c_0_83]), c_0_56]), c_0_57]), c_0_58])]), c_0_59])).
cnf(c_0_162, negated_conjecture, (v4_rlvect_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(spm,[status(thm)],[c_0_136, c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_58])]), c_0_59])).
cnf(c_0_163, negated_conjecture, (v3_rlvect_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(spm,[status(thm)],[c_0_137, c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_58])]), c_0_59])).
cnf(c_0_164, negated_conjecture, (v2_rlvect_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_138, c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_125]), c_0_58])]), c_0_59])).
cnf(c_0_165, negated_conjecture, (v5_group_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_125]), c_0_140]), c_0_58])]), c_0_59])).
cnf(c_0_166, negated_conjecture, (v3_group_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_55]), c_0_61]), c_0_83]), c_0_56]), c_0_57]), c_0_125]), c_0_84]), c_0_58])]), c_0_59])).
cnf(c_0_167, negated_conjecture, (v13_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_142, c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_58])]), c_0_59])).
cnf(c_0_168, negated_conjecture, (v7_struct_0(esk1_0)|v1_vectsp_2(k12_polynom3(esk1_0))|~l2_algstr_0(esk1_0)), 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_143, c_0_144]), c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_58])])).
fof(c_0_169, plain, ![X115, X116]:((~v4_ring_2(X116,X115)|v2_ring_1(k7_ideal_1(X115,k6_domain_1(u1_struct_0(X115),X116)),X115)|(v9_struct_0(X116,X115)|~m1_subset_1(X116,u1_struct_0(X115)))|(v2_struct_0(X115)|v6_struct_0(X115)|~v13_algstr_0(X115)|~v4_vectsp_1(X115)|~v5_vectsp_1(X115)|~v2_rlvect_1(X115)|~v3_rlvect_1(X115)|~v4_rlvect_1(X115)|~v3_group_1(X115)|~v5_group_1(X115)|~l6_algstr_0(X115)))&(~v2_ring_1(k7_ideal_1(X115,k6_domain_1(u1_struct_0(X115),X116)),X115)|v4_ring_2(X116,X115)|(v9_struct_0(X116,X115)|~m1_subset_1(X116,u1_struct_0(X115)))|(v2_struct_0(X115)|v6_struct_0(X115)|~v13_algstr_0(X115)|~v4_vectsp_1(X115)|~v5_vectsp_1(X115)|~v2_rlvect_1(X115)|~v3_rlvect_1(X115)|~v4_rlvect_1(X115)|~v3_group_1(X115)|~v5_group_1(X115)|~l6_algstr_0(X115)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_145])])])])).
cnf(c_0_170, 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_146])).
cnf(c_0_171, plain, (k7_ideal_1(k12_polynom3(X1),k1_ring_4(k12_polynom3(X1),esk8_3(X1,X2,X3)))=k3_algnum_1(X1,X2,X3)|v6_struct_0(X2)|v2_struct_0(X1)|v2_struct_0(X2)|~r1_algnum_1(X1,X2,X3)|~m1_c0sp1(X1,X2)|~m1_subset_1(X3,u1_struct_0(X2))|~l6_algstr_0(X2)|~l6_algstr_0(X1)|~v5_vectsp_1(X2)|~v5_vectsp_1(X1)|~v4_vectsp_1(X2)|~v4_vectsp_1(X1)|~v4_rlvect_1(X2)|~v4_rlvect_1(X1)|~v3_rlvect_1(X2)|~v3_rlvect_1(X1)|~v2_rlvect_1(X2)|~v2_rlvect_1(X1)|~v5_group_1(X2)|~v3_group_1(X2)|~v3_group_1(X1)|~v33_algstr_0(X2)|~v33_algstr_0(X1)|~v13_algstr_0(X2)|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_147, c_0_65]), c_0_66])).
cnf(c_0_172, negated_conjecture, (k1_ring_4(k12_polynom3(esk1_0),esk8_3(esk1_0,esk2_0,esk3_0))=k1_tarski(esk8_3(esk1_0,esk2_0,esk3_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_149]), c_0_150])]), c_0_151])).
cnf(c_0_173, negated_conjecture, (v2_ring_1(k3_algnum_1(X1,esk2_0,esk3_0),k12_polynom3(X1))|v2_struct_0(X1)|~r1_algnum_1(X1,esk2_0,esk3_0)|~m1_c0sp1(X1,esk2_0)|~l6_algstr_0(X1)|~v5_vectsp_1(X1)|~v4_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v2_rlvect_1(X1)|~v3_group_1(X1)|~v33_algstr_0(X1)|~v13_algstr_0(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(spm,[status(thm)],[c_0_152, c_0_90]), c_0_91]), c_0_92]), c_0_93]), c_0_94]), c_0_95]), c_0_96]), c_0_97]), c_0_98]), c_0_99]), c_0_100])]), c_0_101]), c_0_102])).
fof(c_0_174, plain, ![X92, X93]:((~v9_struct_0(X93,X92)|X93=k4_struct_0(X92)|~m1_subset_1(X93,u1_struct_0(X92))|~l2_struct_0(X92))&(X93!=k4_struct_0(X92)|v9_struct_0(X93,X92)|~m1_subset_1(X93,u1_struct_0(X92))|~l2_struct_0(X92))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_struct_0])])])])).
cnf(c_0_175, plain, (k4_struct_0(k12_polynom3(X1))=k8_polynom3(X1)|v2_struct_0(X1)|~l6_algstr_0(X1)|~v5_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_153]), c_0_126]), c_0_154]), c_0_155])).
fof(c_0_176, plain, ![X117, X118]:((~v4_ring_1(k7_ideal_1(X117,k6_domain_1(u1_struct_0(X117),X118)),X117)|v5_ring_2(X118,X117)|(v9_struct_0(X118,X117)|~m1_subset_1(X118,u1_struct_0(X117)))|(v2_struct_0(X117)|v6_struct_0(X117)|~v13_algstr_0(X117)|~v4_vectsp_1(X117)|~v5_vectsp_1(X117)|~v2_rlvect_1(X117)|~v3_rlvect_1(X117)|~v4_rlvect_1(X117)|~v3_group_1(X117)|~v5_group_1(X117)|~v8_ideal_1(X117)|~v1_vectsp_2(X117)|~l6_algstr_0(X117)))&(~v5_ring_2(X118,X117)|v4_ring_1(k7_ideal_1(X117,k6_domain_1(u1_struct_0(X117),X118)),X117)|(v9_struct_0(X118,X117)|~m1_subset_1(X118,u1_struct_0(X117)))|(v2_struct_0(X117)|v6_struct_0(X117)|~v13_algstr_0(X117)|~v4_vectsp_1(X117)|~v5_vectsp_1(X117)|~v2_rlvect_1(X117)|~v3_rlvect_1(X117)|~v4_rlvect_1(X117)|~v3_group_1(X117)|~v5_group_1(X117)|~v8_ideal_1(X117)|~v1_vectsp_2(X117)|~l6_algstr_0(X117)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])])])).
cnf(c_0_177, plain, (v8_ideal_1(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)|~v1_int_3(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_157])).
cnf(c_0_178, negated_conjecture, (v1_int_3(k12_polynom3(esk1_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(spm,[status(thm)],[c_0_158, c_0_55]), c_0_61]), c_0_83]), c_0_56]), c_0_57]), c_0_125]), c_0_140]), c_0_84]), c_0_85]), c_0_58])]), c_0_127]), c_0_59])).
cnf(c_0_179, negated_conjecture, (v5_ring_2(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|v6_struct_0(k12_polynom3(esk1_0))|~v4_ring_2(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|~v1_vectsp_2(k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_149]), c_0_150]), c_0_160]), c_0_161]), c_0_162]), c_0_163]), c_0_164]), c_0_165]), c_0_166]), c_0_167])]), c_0_151])).
cnf(c_0_180, negated_conjecture, (v7_struct_0(esk1_0)|v1_vectsp_2(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_45]), c_0_55])])).
cnf(c_0_181, plain, (v4_ring_2(X2,X1)|v9_struct_0(X2,X1)|v2_struct_0(X1)|v6_struct_0(X1)|~v2_ring_1(k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),X2)),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_169])).
cnf(c_0_182, negated_conjecture, (k6_domain_1(u1_struct_0(k12_polynom3(esk1_0)),esk8_3(esk1_0,esk2_0,esk3_0))=k1_tarski(esk8_3(esk1_0,esk2_0,esk3_0))|v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))), inference(spm,[status(thm)],[c_0_170, c_0_149])).
cnf(c_0_183, negated_conjecture, (k7_ideal_1(k12_polynom3(esk1_0),k1_tarski(esk8_3(esk1_0,esk2_0,esk3_0)))=k3_algnum_1(esk1_0,esk2_0,esk3_0)), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171, c_0_172]), c_0_123]), c_0_124]), c_0_90]), c_0_91]), c_0_55]), c_0_92]), c_0_61]), c_0_93]), c_0_83]), c_0_94]), c_0_56]), c_0_95]), c_0_57]), c_0_96]), c_0_125]), c_0_97]), c_0_98]), c_0_84]), c_0_99]), c_0_85]), c_0_100]), c_0_58])]), c_0_101]), c_0_102]), c_0_59])).
cnf(c_0_184, negated_conjecture, (v2_ring_1(k3_algnum_1(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173, c_0_123]), c_0_124]), c_0_55]), c_0_61]), c_0_83]), c_0_56]), c_0_57]), c_0_125]), c_0_84]), c_0_85]), c_0_58])]), c_0_59])).
cnf(c_0_185, plain, (X1=k4_struct_0(X2)|~v9_struct_0(X1,X2)|~m1_subset_1(X1,u1_struct_0(X2))|~l2_struct_0(X2)), inference(split_conjunct,[status(thm)],[c_0_174])).
cnf(c_0_186, negated_conjecture, (k4_struct_0(k12_polynom3(esk1_0))=k8_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_175, c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_58])]), c_0_59])).
fof(c_0_187, plain, ![X95]:((l2_struct_0(X95)|~l2_algstr_0(X95))&(l1_algstr_0(X95)|~l2_algstr_0(X95))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])).
cnf(c_0_188, plain, (v4_ring_1(k7_ideal_1(X2,k6_domain_1(u1_struct_0(X2),X1)),X2)|v9_struct_0(X1,X2)|v2_struct_0(X2)|v6_struct_0(X2)|~v5_ring_2(X1,X2)|~m1_subset_1(X1,u1_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)|~v5_group_1(X2)|~v8_ideal_1(X2)|~v1_vectsp_2(X2)|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_176])).
cnf(c_0_189, negated_conjecture, (v8_ideal_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177, c_0_178]), c_0_150]), c_0_160]), c_0_161]), c_0_162]), c_0_163]), c_0_164]), c_0_165]), c_0_166]), c_0_167])]), c_0_151])).
cnf(c_0_190, negated_conjecture, (~v4_ring_1(k3_algnum_1(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_46])).
cnf(c_0_191, negated_conjecture, (v5_ring_2(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))|~v4_ring_2(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))), inference(spm,[status(thm)],[c_0_179, c_0_180])).
cnf(c_0_192, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|v9_struct_0(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|v4_ring_2(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|v6_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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_181, c_0_182]), c_0_149]), c_0_150]), c_0_160]), c_0_161]), c_0_162]), c_0_163]), c_0_164]), c_0_165]), c_0_166]), c_0_167])]), c_0_151]), c_0_183]), c_0_184])])).
cnf(c_0_193, negated_conjecture, (X1=k8_polynom3(esk1_0)|~v9_struct_0(X1,k12_polynom3(esk1_0))|~l2_struct_0(k12_polynom3(esk1_0))|~m1_subset_1(X1,u1_struct_0(k12_polynom3(esk1_0)))), inference(spm,[status(thm)],[c_0_185, c_0_186])).
cnf(c_0_194, plain, (l2_struct_0(X1)|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_187])).
cnf(c_0_195, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|v9_struct_0(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|v6_struct_0(k12_polynom3(esk1_0))|~v5_ring_2(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|~v1_vectsp_2(k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(rw,[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_188, c_0_182]), c_0_189]), c_0_149]), c_0_150]), c_0_160]), c_0_161]), c_0_162]), c_0_163]), c_0_164]), c_0_165]), c_0_166]), c_0_167])]), c_0_151]), c_0_183]), c_0_190])).
cnf(c_0_196, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|v9_struct_0(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|v5_ring_2(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))), inference(spm,[status(thm)],[c_0_191, c_0_192])).
fof(c_0_197, 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_198, negated_conjecture, (X1=k8_polynom3(esk1_0)|~v9_struct_0(X1,k12_polynom3(esk1_0))|~l2_algstr_0(k12_polynom3(esk1_0))|~m1_subset_1(X1,u1_struct_0(k12_polynom3(esk1_0)))), inference(spm,[status(thm)],[c_0_193, c_0_194])).
cnf(c_0_199, negated_conjecture, (v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|v9_struct_0(esk8_3(esk1_0,esk2_0,esk3_0),k12_polynom3(esk1_0))|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_195, c_0_180]), c_0_196])).
fof(c_0_200, plain, ![X106]:(v2_struct_0(X106)|~l1_struct_0(X106)|~v1_xboole_0(u1_struct_0(X106))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_197])])).
cnf(c_0_201, negated_conjecture, (esk8_3(esk1_0,esk2_0,esk3_0)=k8_polynom3(esk1_0)|v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))|~l2_algstr_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198, c_0_199]), c_0_149])])).
cnf(c_0_202, plain, (v2_struct_0(X1)|~l1_struct_0(X1)|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_200])).
cnf(c_0_203, negated_conjecture, (esk8_3(esk1_0,esk2_0,esk3_0)=k8_polynom3(esk1_0)|v1_xboole_0(u1_struct_0(k12_polynom3(esk1_0)))|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201, c_0_45]), c_0_150])])).
fof(c_0_204, plain, ![X96]:(~l2_struct_0(X96)|l1_struct_0(X96)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])).
fof(c_0_205, plain, ![X1]:(l4_struct_0(X1)=>(~v6_struct_0(X1)=>~v7_struct_0(X1))), inference(fof_simplification,[status(thm)],[cc3_struct_0])).
cnf(c_0_206, negated_conjecture, (esk8_3(esk1_0,esk2_0,esk3_0)=k8_polynom3(esk1_0)|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))|~l1_struct_0(k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_202, c_0_203]), c_0_151])).
cnf(c_0_207, plain, (l1_struct_0(X1)|~l2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_204])).
fof(c_0_208, plain, ![X78]:(~l4_struct_0(X78)|(v6_struct_0(X78)|~v7_struct_0(X78))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_205])])).
fof(c_0_209, plain, ![X97]:((l4_algstr_0(X97)|~l5_algstr_0(X97))&(l4_struct_0(X97)|~l5_algstr_0(X97))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_algstr_0])])])).
cnf(c_0_210, plain, (v2_struct_0(X2)|v6_struct_0(X2)|v2_struct_0(X1)|v6_struct_0(X1)|esk8_3(X1,X2,X3)!=k8_polynom3(X1)|~m1_c0sp1(X1,X2)|~r1_algnum_1(X1,X2,X3)|~m1_subset_1(X3,u1_struct_0(X2))|~v13_algstr_0(X2)|~v33_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)|~v5_group_1(X2)|~l6_algstr_0(X2)|~v13_algstr_0(X1)|~v33_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)|~v5_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_50])).
cnf(c_0_211, negated_conjecture, (esk8_3(esk1_0,esk2_0,esk3_0)=k8_polynom3(esk1_0)|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))|~l2_struct_0(k12_polynom3(esk1_0))), inference(spm,[status(thm)],[c_0_206, c_0_207])).
cnf(c_0_212, plain, (v6_struct_0(X1)|~l4_struct_0(X1)|~v7_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_208])).
cnf(c_0_213, plain, (l4_struct_0(X1)|~l5_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_209])).
cnf(c_0_214, plain, (v6_struct_0(X1)|v2_struct_0(X2)|v2_struct_0(X1)|esk8_3(X2,X1,X3)!=k8_polynom3(X2)|~r1_algnum_1(X2,X1,X3)|~m1_c0sp1(X2,X1)|~m1_subset_1(X3,u1_struct_0(X1))|~l6_algstr_0(X1)|~l6_algstr_0(X2)|~v5_vectsp_1(X1)|~v5_vectsp_1(X2)|~v4_vectsp_1(X1)|~v4_vectsp_1(X2)|~v4_rlvect_1(X1)|~v4_rlvect_1(X2)|~v3_rlvect_1(X1)|~v3_rlvect_1(X2)|~v2_rlvect_1(X1)|~v2_rlvect_1(X2)|~v5_group_1(X1)|~v3_group_1(X1)|~v3_group_1(X2)|~v33_algstr_0(X1)|~v33_algstr_0(X2)|~v13_algstr_0(X1)|~v13_algstr_0(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_210, c_0_65]), c_0_66])).
cnf(c_0_215, negated_conjecture, (esk8_3(esk1_0,esk2_0,esk3_0)=k8_polynom3(esk1_0)|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))|~l2_algstr_0(k12_polynom3(esk1_0))), inference(spm,[status(thm)],[c_0_211, c_0_194])).
cnf(c_0_216, plain, (v6_struct_0(X1)|~l5_algstr_0(X1)|~v7_struct_0(X1)), inference(spm,[status(thm)],[c_0_212, c_0_213])).
cnf(c_0_217, plain, (l5_algstr_0(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_37])).
cnf(c_0_218, negated_conjecture, (v2_struct_0(X1)|esk8_3(X1,esk2_0,esk3_0)!=k8_polynom3(X1)|~r1_algnum_1(X1,esk2_0,esk3_0)|~m1_c0sp1(X1,esk2_0)|~l6_algstr_0(X1)|~v5_vectsp_1(X1)|~v4_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v2_rlvect_1(X1)|~v3_group_1(X1)|~v33_algstr_0(X1)|~v13_algstr_0(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(spm,[status(thm)],[c_0_214, c_0_90]), c_0_91]), c_0_92]), c_0_93]), c_0_94]), c_0_95]), c_0_96]), c_0_97]), c_0_98]), c_0_99]), c_0_100])]), c_0_101]), c_0_102])).
cnf(c_0_219, negated_conjecture, (esk8_3(esk1_0,esk2_0,esk3_0)=k8_polynom3(esk1_0)|v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215, c_0_45]), c_0_150])])).
cnf(c_0_220, plain, (v6_struct_0(X1)|~v7_struct_0(X1)|~l6_algstr_0(X1)), inference(spm,[status(thm)],[c_0_216, c_0_217])).
cnf(c_0_221, negated_conjecture, (v7_struct_0(esk1_0)|v6_struct_0(k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218, c_0_219]), c_0_123]), c_0_124]), c_0_55]), c_0_61]), c_0_83]), c_0_56]), c_0_57]), c_0_125]), c_0_84]), c_0_85]), c_0_58])]), c_0_59])).
cnf(c_0_222, plain, (v6_struct_0(X1)|~v6_struct_0(k12_polynom3(X1))|~v13_algstr_0(X1)|~v5_vectsp_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_104])).
cnf(c_0_223, negated_conjecture, (v6_struct_0(k12_polynom3(esk1_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220, c_0_221]), c_0_55])]), c_0_127])).
cnf(c_0_224, 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_222, c_0_223]), c_0_55]), c_0_61]), c_0_56]), c_0_57]), c_0_58])]), c_0_127]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 225
# Proof object clause steps            : 124
# Proof object formula steps           : 101
# Proof object conjectures             : 77
# Proof object clause conjectures      : 74
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 69
# Proof object initial formulas used   : 35
# Proof object generating inferences   : 50
# Proof object simplifying inferences  : 302
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 35
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 193
# Removed in clause preprocessing      : 18
# Initial clauses in saturation        : 175
# Processed clauses                    : 855
# ...of these trivial                  : 1
# ...subsumed                          : 30
# ...remaining for further processing  : 824
# Other redundant clauses eliminated   : 9
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 83
# Backward-rewritten                   : 34
# Generated clauses                    : 1241
# ...of the previous two non-trivial   : 1135
# Contextual simplify-reflections      : 476
# Paramodulations                      : 1235
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 9
# 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  : 544
#    Positive orientable unit clauses  : 102
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 7
#    Non-unit-clauses                  : 435
# Current number of unprocessed clauses: 587
# ...number of literals in the above   : 5324
# Current number of archived formulas  : 0
# Current number of archived clauses   : 274
# Clause-clause subsumption calls (NU) : 157432
# Rec. Clause-clause subsumption calls : 9668
# Non-unit clause-clause subsumptions  : 587
# Unit Clause-clause subsumption calls : 2595
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 16
# BW rewrite match successes           : 4
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 85261

# -------------------------------------------------
# User time                : 0.099 s
# System time              : 0.008 s
# Total time               : 0.107 s
# Maximum resident set size: 3328 pages
