% Mizar problem: t26_polyred,polyred,1847,52 
fof(t26_polyred,conjecture,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_rlvect_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ( ( r1_polyred(A,B,C,D,E)
                          & r1_polyred(A,B,C,E,D) )
                      <=> k12_polynom1(k14_polynom1(A),C,D) = k12_polynom1(k14_polynom1(A),C,E) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc10_rewrite1,cc11_rewrite1,cc12_rewrite1,cc13_rewrite1,cc14_rewrite1,cc15_rewrite1,cc1_finseq_1,cc1_finset_1,cc1_finsub_1,cc1_relat_1,cc1_relset_1,cc2_finset_1,cc2_finsub_1,cc2_rewrite1,cc3_finsub_1,cc3_polynom1,cc3_rewrite1,cc4_rewrite1,cc5_polynom1,cc5_rewrite1,cc6_rewrite1,cc7_rewrite1,cc8_rewrite1,cc9_rewrite1,d2_polyred,dt_g1_orders_2,dt_k12_polynom1,dt_k13_bagorder,dt_k13_polynom1,dt_k14_polynom1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k5_finsub_1,dt_l1_orders_2,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc1_finsub_1,fc1_orders_2,fc1_struct_0,fc20_polynom1,fc25_polynom1,fc2_finseq_1,fc2_finsub_1,fc2_orders_2,fc3_orders_2,fc3_polynom1,fc3_polyred,fc4_relat_1,free_g1_orders_2,l35_polyred,rc11_polynom1,rc14_polynom1,rc1_finseq_1,rc1_finset_1,rc1_orders_2,rc1_relat_1,rc1_rewrite1,rc2_orders_2,rc2_polynom1,rc2_relat_1,rc2_rewrite1,rc3_finseq_1,rc3_finset_1,rc3_relat_1,rc3_rewrite1,rc3_struct_0,rc4_finset_1,rc4_rewrite1,rc4_struct_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc7_polynom1,rc8_finseq_1,redefinition_k14_polynom1,redefinition_m2_relset_1,reflexivity_r1_tarski,t12_orders_1,t13_orders_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(polyred,t26_polyred)]).

fof(abstractness_v1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_orders_2(A)
       => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ),
    file(orders_2,v1_orders_2),
    []).

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

fof(cc10_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v5_rewrite1(A) )
     => ( v1_relat_1(A)
        & v4_rewrite1(A) ) ) ),
    file(rewrite1,cc10_rewrite1),
    []).

fof(cc11_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_rewrite1(A)
        & v4_rewrite1(A) )
     => ( v1_relat_1(A)
        & v8_rewrite1(A) ) ) ),
    file(rewrite1,cc11_rewrite1),
    []).

fof(cc12_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(A) )
     => ( v1_relat_1(A)
        & v4_rewrite1(A)
        & v5_rewrite1(A)
        & v6_rewrite1(A)
        & v7_rewrite1(A)
        & v8_rewrite1(A)
        & v9_rewrite1(A) ) ) ),
    file(rewrite1,cc12_rewrite1),
    []).

fof(cc13_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_rewrite1(A)
        & v9_rewrite1(A) )
     => ( v1_relat_1(A)
        & v4_rewrite1(A)
        & v5_rewrite1(A)
        & v7_rewrite1(A)
        & v8_rewrite1(A)
        & v9_rewrite1(A) ) ) ),
    file(rewrite1,cc13_rewrite1),
    []).

fof(cc14_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v10_rewrite1(A) )
     => ( v1_relat_1(A)
        & v2_relat_2(A)
        & v1_rewrite1(A)
        & v2_rewrite1(A)
        & v3_rewrite1(A)
        & v4_rewrite1(A)
        & v5_rewrite1(A)
        & v7_rewrite1(A)
        & v8_rewrite1(A)
        & v9_rewrite1(A) ) ) ),
    file(rewrite1,cc14_rewrite1),
    []).

fof(cc15_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_rewrite1(A)
        & v7_rewrite1(A) )
     => ( v1_relat_1(A)
        & v10_rewrite1(A) ) ) ),
    file(rewrite1,cc15_rewrite1),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

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

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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(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_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

fof(cc2_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_rewrite1(A) )
     => ( v1_relat_1(A)
        & v2_relat_2(A)
        & v1_rewrite1(A) ) ) ),
    file(rewrite1,cc2_rewrite1),
    []).

fof(cc3_finsub_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
     => v1_finset_1(B) ) ),
    file(finsub_1,cc3_finsub_1),
    []).

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_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_2(A)
        & v1_rewrite1(A) )
     => ( v1_relat_1(A)
        & v3_rewrite1(A) ) ) ),
    file(rewrite1,cc3_rewrite1),
    []).

fof(cc4_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(A) )
     => ( v1_relat_1(A)
        & v2_relat_2(A)
        & v1_rewrite1(A)
        & v2_rewrite1(A)
        & v3_rewrite1(A) ) ) ),
    file(rewrite1,cc4_rewrite1),
    []).

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_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v3_rewrite1(A) )
     => ( v1_relat_1(A)
        & v2_rewrite1(A) ) ) ),
    file(rewrite1,cc5_rewrite1),
    []).

fof(cc6_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v8_rewrite1(A) )
     => ( v1_relat_1(A)
        & v7_rewrite1(A) ) ) ),
    file(rewrite1,cc6_rewrite1),
    []).

fof(cc7_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v7_rewrite1(A) )
     => ( v1_relat_1(A)
        & v8_rewrite1(A)
        & v9_rewrite1(A) ) ) ),
    file(rewrite1,cc7_rewrite1),
    []).

fof(cc8_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v6_rewrite1(A) )
     => ( v1_relat_1(A)
        & v7_rewrite1(A) ) ) ),
    file(rewrite1,cc8_rewrite1),
    []).

fof(cc9_rewrite1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v8_rewrite1(A) )
     => ( v1_relat_1(A)
        & v5_rewrite1(A) ) ) ),
    file(rewrite1,cc9_rewrite1),
    []).

fof(d2_polyred,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l2_struct_0(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
                        & v2_polynom1(E,k14_polynom1(A),C)
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ( r1_polyred(A,B,C,D,E)
                      <=> r2_hidden(k4_tarski(k12_polynom1(k14_polynom1(A),C,D),k12_polynom1(k14_polynom1(A),C,E)),k13_bagorder(g1_orders_2(k14_polynom1(A),B))) ) ) ) ) ) ) ),
    file(polyred,d2_polyred),
    []).

fof(dt_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( v1_orders_2(g1_orders_2(A,B))
        & l1_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(dt_k12_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & l2_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,u1_struct_0(B))
        & m1_relset_1(C,A,u1_struct_0(B)) )
     => m1_subset_1(k12_polynom1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(polynom1,k12_polynom1),
    []).

fof(dt_k13_bagorder,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( v1_partfun1(k13_bagorder(A),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))
        & v1_relat_2(k13_bagorder(A))
        & v4_relat_2(k13_bagorder(A))
        & v8_relat_2(k13_bagorder(A))
        & m2_relset_1(k13_bagorder(A),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))) ) ) ),
    file(bagorder,k13_bagorder),
    []).

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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

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_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

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_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(orders_2,u1_orders_2),
    []).

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

fof(existence_l1_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

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_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

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(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_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_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    []).

fof(fc1_orders_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,A) )
     => ( ~ v3_struct_0(g1_orders_2(A,B))
        & v1_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,fc1_orders_2),
    []).

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(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & 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_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A)) ) ),
    file(finsub_1,fc2_finsub_1),
    []).

fof(fc2_orders_2,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(u1_orders_2(A))
        & v1_relat_2(u1_orders_2(A))
        & v4_relat_2(u1_orders_2(A))
        & v8_relat_2(u1_orders_2(A))
        & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(orders_2,fc2_orders_2),
    []).

fof(fc3_orders_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => ( v1_orders_2(g1_orders_2(A,B))
        & v2_orders_2(g1_orders_2(A,B))
        & v3_orders_2(g1_orders_2(A,B))
        & v4_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,fc3_orders_2),
    []).

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(fc3_polyred,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v1_relat_2(B)
        & v4_relat_2(B)
        & v6_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
        & m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
     => ( ~ v3_struct_0(g1_orders_2(k14_polynom1(A),B))
        & v1_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v2_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v3_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v4_orders_2(g1_orders_2(k14_polynom1(A),B))
        & v16_waybel_0(g1_orders_2(k14_polynom1(A),B)) ) ) ),
    file(polyred,fc3_polyred),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(free_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ! [C,D] : 
          ( g1_orders_2(A,B) = g1_orders_2(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(l35_polyred,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_relat_2(B)
            & v4_relat_2(B)
            & v6_relat_2(B)
            & v8_relat_2(B)
            & v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
            & m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l2_struct_0(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & v2_polynom1(D,k14_polynom1(A),C)
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => r2_hidden(k12_polynom1(k14_polynom1(A),C,D),k5_finsub_1(u1_struct_0(g1_orders_2(k14_polynom1(A),B)))) ) ) ) ) ),
    file(polyred,l35_polyred),
    []).

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_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

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

fof(rc1_orders_2,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & v1_orders_2(A) ) ),
    file(orders_2,rc1_orders_2),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc1_rewrite1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v2_relat_2(A)
      & v1_rewrite1(A)
      & v2_rewrite1(A)
      & v3_rewrite1(A) ) ),
    file(rewrite1,rc1_rewrite1),
    []).

fof(rc2_orders_2,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A) ) ),
    file(orders_2,rc2_orders_2),
    []).

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_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

fof(rc2_rewrite1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v2_relat_2(A)
      & v1_rewrite1(A)
      & v2_rewrite1(A)
      & v3_rewrite1(A)
      & v4_rewrite1(A)
      & v5_rewrite1(A)
      & v6_rewrite1(A)
      & v7_rewrite1(A)
      & v8_rewrite1(A)
      & v9_rewrite1(A) ) ),
    file(rewrite1,rc2_rewrite1),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    []).

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_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc3_rewrite1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v2_relat_2(A)
      & v1_rewrite1(A)
      & v2_rewrite1(A)
      & v3_rewrite1(A)
      & v4_rewrite1(A)
      & v5_rewrite1(A)
      & v6_rewrite1(A)
      & v7_rewrite1(A)
      & v8_rewrite1(A)
      & v9_rewrite1(A)
      & v10_rewrite1(A) ) ),
    file(rewrite1,rc3_rewrite1),
    []).

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_rewrite1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v2_relat_2(A)
      & v1_rewrite1(A)
      & v2_rewrite1(A)
      & v3_rewrite1(A)
      & v4_rewrite1(A)
      & v5_rewrite1(A)
      & v7_rewrite1(A)
      & v8_rewrite1(A)
      & v9_rewrite1(A)
      & v10_rewrite1(A) ) ),
    file(rewrite1,rc4_rewrite1),
    []).

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(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

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(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k14_polynom1,axiom,(
    ! [A] : k14_polynom1(A) = k13_polynom1(A) ),
    file(polynom1,k14_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(t12_orders_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_2(C)
        & v4_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ( r2_hidden(B,A)
       => r2_hidden(k4_tarski(B,B),C) ) ) ),
    file(orders_1,t12_orders_1),
    []).

fof(t13_orders_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_relat_2(D)
        & v4_relat_2(D)
        & v8_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( ( r2_hidden(B,A)
          & r2_hidden(C,A)
          & r2_hidden(k4_tarski(B,C),D)
          & r2_hidden(k4_tarski(C,B),D) )
       => B = C ) ) ),
    file(orders_1,t13_orders_1),
    []).

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

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