% Mizar problem: t12_groeb_3,groeb_3,359,33 
fof(t12_groeb_3,conjecture,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v2_group_1(B)
            & v7_group_1(B)
            & v7_vectsp_1(B)
            & ~ v3_realset2(B)
            & l3_vectsp_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
                & v2_polynom1(C,k14_polynom1(A),B)
                & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                    & v2_polynom1(D,k14_polynom1(A),B)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
                 => ( k25_polynom1(A,B,C,D) = k26_polynom1(A,B)
                   => C = D ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_algstr_1,cc1_binom,cc1_finset_1,cc1_polynom7,cc1_relset_1,cc1_vectsp_1,cc2_algstr_1,cc2_binom,cc2_finset_1,cc2_vectsp_1,cc3_algstr_1,cc3_binom,cc3_polynom1,cc3_polynom7,cc3_vectsp_1,cc4_algstr_1,cc4_binom,cc4_polynom7,cc4_vectsp_1,cc5_binom,cc5_polynom1,cc5_vectsp_1,commutativity_k23_polynom1,d23_polynom1,dt_k13_polynom1,dt_k14_polynom1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_polynom1,dt_k23_polynom1,dt_k24_polynom1,dt_k25_polynom1,dt_k26_polynom1,dt_k2_zfmisc_1,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc14_finset_1,fc14_polynom1,fc1_polynom2,fc1_polynom7,fc1_struct_0,fc20_polynom1,fc25_polynom1,fc32_polynom1,fc33_polynom1,fc35_polynom1,fc3_polynom1,involutiveness_k24_polynom1,rc11_polynom1,rc14_polynom1,rc1_binom,rc1_finset_1,rc1_polynom7,rc1_termord,rc2_binom,rc2_polynom1,rc2_termord,rc3_binom,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc4_struct_0,rc5_struct_0,rc7_polynom1,rc7_polynom7,rc8_polynom7,redefinition_k14_polynom1,redefinition_k23_polynom1,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_polyred,t2_subset,t3_polyred,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t80_polynom1,t82_polynom1,t8_boole]),
    [file(groeb_3,t12_groeb_3)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) ) ) ) ),
    file(algstr_1,cc1_algstr_1),
    []).

fof(cc1_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_binom(A) ) ) ) ),
    file(binom,cc1_binom),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_polynom7,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => ( ~ v3_realset2(A)
       => ~ v3_struct_0(A) ) ) ),
    file(polynom7,cc1_polynom7),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc1_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc1_vectsp_1),
    []).

fof(cc2_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc2_algstr_1),
    []).

fof(cc2_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_binom(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A) ) ) ) ),
    file(binom,cc2_binom),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc2_vectsp_1),
    []).

fof(cc3_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_rlvect_1(A) ) ) ) ),
    file(algstr_1,cc3_algstr_1),
    []).

fof(cc3_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v3_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A) ) ) ) ),
    file(binom,cc3_binom),
    []).

fof(cc3_polynom1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v7_seqm_3(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) ) ) ),
    file(polynom1,cc3_polynom1),
    []).

fof(cc3_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
              & v3_polynom7(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
              & v2_polynom1(C,k14_polynom1(A),B) ) ) ) ) ),
    file(polynom7,cc3_polynom7),
    []).

fof(cc3_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc3_vectsp_1),
    []).

fof(cc4_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_algstr_1(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc4_algstr_1),
    []).

fof(cc4_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v2_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v3_algstr_1(A) ) ) ) ),
    file(binom,cc4_binom),
    []).

fof(cc4_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
              & v4_polynom7(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
              & v2_polynom1(C,k14_polynom1(A),B)
              & v3_polynom7(C,A,B) ) ) ) ) ),
    file(polynom7,cc4_polynom7),
    []).

fof(cc4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(vectsp_1,cc4_vectsp_1),
    []).

fof(cc5_binom,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A) )
       => ( ~ v3_struct_0(A)
          & v3_algstr_1(A) ) ) ) ),
    file(binom,cc5_binom),
    []).

fof(cc5_polynom1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_polynom1(A) ) ) ),
    file(polynom1,cc5_polynom1),
    []).

fof(cc5_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc5_vectsp_1),
    []).

fof(commutativity_k23_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v5_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => k23_polynom1(A,B,C,D) = k23_polynom1(A,B,D,C) ) ),
    file(polynom1,k23_polynom1),
    []).

fof(d23_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
             => k25_polynom1(A,B,C,D) = k22_polynom1(A,B,C,k24_polynom1(A,B,D)) ) ) ) ),
    file(polynom1,d23_polynom1),
    []).

fof(dt_k13_polynom1,axiom,(
    $true ),
    file(polynom1,k13_polynom1),
    []).

fof(dt_k14_polynom1,axiom,(
    ! [A] : m1_subset_1(k14_polynom1(A),k1_zfmisc_1(k13_polynom1(A))) ),
    file(polynom1,k14_polynom1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k22_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_funct_1(k22_polynom1(A,B,C,D))
        & v1_funct_2(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & m2_relset_1(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ),
    file(polynom1,k22_polynom1),
    []).

fof(dt_k23_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v5_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_funct_1(k23_polynom1(A,B,C,D))
        & v1_funct_2(k23_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & m2_relset_1(k23_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ),
    file(polynom1,k23_polynom1),
    []).

fof(dt_k24_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_funct_1(k24_polynom1(A,B,C))
        & v1_funct_2(k24_polynom1(A,B,C),k14_polynom1(A),u1_struct_0(B))
        & m2_relset_1(k24_polynom1(A,B,C),k14_polynom1(A),u1_struct_0(B)) ) ) ),
    file(polynom1,k24_polynom1),
    []).

fof(dt_k25_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_funct_1(k25_polynom1(A,B,C,D))
        & v1_funct_2(k25_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & m2_relset_1(k25_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ),
    file(polynom1,k25_polynom1),
    []).

fof(dt_k26_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ( v1_funct_1(k26_polynom1(A,B))
        & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
        & m2_relset_1(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) ) ) ),
    file(polynom1,k26_polynom1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_l2_vectsp_1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(dt_l3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_l2_vectsp_1,axiom,(
    ? [A] : l2_vectsp_1(A) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(existence_l3_vectsp_1,axiom,(
    ? [A] : l3_vectsp_1(A) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

fof(fc14_polynom1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0) ),
    file(polynom1,fc14_polynom1),
    []).

fof(fc1_polynom2,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(D,k14_polynom1(A),B)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_relat_1(k25_polynom1(A,B,C,D))
        & v1_funct_1(k25_polynom1(A,B,C,D))
        & v1_funct_2(k25_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k25_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) ),
    file(polynom2,fc1_polynom2),
    []).

fof(fc1_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ( v1_relat_1(k26_polynom1(A,B))
        & v1_funct_1(k26_polynom1(A,B))
        & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k26_polynom1(A,B),k14_polynom1(A),B)
        & v3_polynom7(k26_polynom1(A,B),A,B)
        & v4_polynom7(k26_polynom1(A,B),A,B) ) ) ),
    file(polynom7,fc1_polynom7),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc20_polynom1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_seq_1(k1_xboole_0)
    & v1_matrlin(k1_xboole_0)
    & v7_seqm_3(k1_xboole_0)
    & v1_polynom1(k1_xboole_0) ),
    file(polynom1,fc20_polynom1),
    []).

fof(fc25_polynom1,axiom,(
    ! [A] : ~ v1_xboole_0(k13_polynom1(A)) ),
    file(polynom1,fc25_polynom1),
    []).

fof(fc32_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v5_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(D,k14_polynom1(A),B)
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_relat_1(k22_polynom1(A,B,C,D))
        & v1_funct_1(k22_polynom1(A,B,C,D))
        & v1_funct_2(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k22_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) ),
    file(polynom1,fc32_polynom1),
    []).

fof(fc33_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(C,k14_polynom1(A),B)
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
     => ( v1_relat_1(k24_polynom1(A,B,C))
        & v1_funct_1(k24_polynom1(A,B,C))
        & v1_funct_2(k24_polynom1(A,B,C),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k24_polynom1(A,B,C),k14_polynom1(A),B) ) ) ),
    file(polynom1,fc33_polynom1),
    []).

fof(fc35_polynom1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ( v1_relat_1(k26_polynom1(A,B))
        & v1_funct_1(k26_polynom1(A,B))
        & v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
        & v2_polynom1(k26_polynom1(A,B),k14_polynom1(A),B) ) ) ),
    file(polynom1,fc35_polynom1),
    []).

fof(fc3_polynom1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0)
    & v1_matrlin(k1_xboole_0) ),
    file(polynom1,fc3_polynom1),
    []).

fof(involutiveness_k24_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
     => k24_polynom1(A,B,k24_polynom1(A,B,C)) = C ) ),
    file(polynom1,k24_polynom1),
    []).

fof(rc11_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_seq_1(A)
      & v7_seqm_3(A)
      & v1_polynom1(A) ) ),
    file(polynom1,rc11_polynom1),
    []).

fof(rc14_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
          & v2_polynom1(C,k14_polynom1(A),B) ) ) ),
    file(polynom1,rc14_polynom1),
    []).

fof(rc1_binom,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v2_algstr_1(A) ) ),
    file(binom,rc1_binom),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_polynom7,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A) ) ),
    file(polynom7,rc1_polynom7),
    []).

fof(rc1_termord,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A) ) ),
    file(termord,rc1_termord),
    []).

fof(rc2_binom,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v3_algstr_1(A) ) ),
    file(binom,rc2_binom),
    []).

fof(rc2_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v1_funcop_1(A)
      & v1_matrlin(A) ) ),
    file(polynom1,rc2_polynom1),
    []).

fof(rc2_termord,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v1_algstr_1(A)
      & v2_algstr_1(A)
      & v3_algstr_1(A)
      & v4_algstr_1(A)
      & v5_algstr_1(A)
      & v6_algstr_1(A)
      & ~ v3_realset2(A) ) ),
    file(termord,rc2_termord),
    []).

fof(rc3_binom,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v1_binom(A) ) ),
    file(binom,rc3_binom),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc7_polynom1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A)
      & v7_seqm_3(A) ) ),
    file(polynom1,rc7_polynom1),
    []).

fof(rc7_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
          & v3_polynom7(C,A,B) ) ) ),
    file(polynom7,rc7_polynom7),
    []).

fof(rc8_polynom7,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
          & v4_polynom7(C,A,B) ) ) ),
    file(polynom7,rc8_polynom7),
    []).

fof(redefinition_k14_polynom1,axiom,(
    ! [A] : k14_polynom1(A) = k13_polynom1(A) ),
    file(polynom1,k14_polynom1),
    []).

fof(redefinition_k23_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v5_rlvect_1(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
     => k23_polynom1(A,B,C,D) = k22_polynom1(A,B,C,D) ) ),
    file(polynom1,k23_polynom1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_polyred,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v1_algstr_1(B)
        & l1_rlvect_1(B) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => k22_polynom1(A,B,k26_polynom1(A,B),C) = C ) ) ),
    file(polyred,t2_polyred),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t3_polyred,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => ( k22_polynom1(A,B,k24_polynom1(A,B,C),C) = k26_polynom1(A,B)
            & k22_polynom1(A,B,C,k24_polynom1(A,B,C)) = k26_polynom1(A,B) ) ) ) ),
    file(polyred,t3_polyred),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t80_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & l3_vectsp_1(B) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
                & m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,k14_polynom1(A),u1_struct_0(B))
                    & m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) )
                 => k22_polynom1(A,B,k22_polynom1(A,B,C,D),E) = k22_polynom1(A,B,C,k22_polynom1(A,B,D,E)) ) ) ) ) ),
    file(polynom1,t80_polynom1),
    []).

fof(t82_polynom1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v5_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
            & m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
         => k22_polynom1(A,B,C,k26_polynom1(A,B)) = C ) ) ),
    file(polynom1,t82_polynom1),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).