% Mizar problem: t18_polyred,polyred,1312,35 
fof(t18_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)
                & l2_struct_0(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
                    & m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
                 => ! [E] : 
                      ( ( v7_seqm_3(E)
                        & v1_polynom1(E)
                        & m1_pboole(E,A) )
                     => ! [F] : 
                          ( ( v7_seqm_3(F)
                            & v1_polynom1(F)
                            & m1_pboole(F,A) )
                         => k1_polyred(A,k9_polynom1(A,E,F),C,D) = k1_polyred(A,E,C,k1_polyred(A,F,C,D)) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[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_polynom1,cc3_rewrite1,cc4_rewrite1,cc5_polynom1,cc5_rewrite1,cc6_polynom1,cc6_rewrite1,cc7_rewrite1,cc8_rewrite1,cc9_rewrite1,commutativity_k9_polynom1,d14_polynom1,d1_funct_2,d1_polyred,dt_k10_polynom1,dt_k13_polynom1,dt_k14_polynom1,dt_k15_polynom1,dt_k1_funct_1,dt_k1_polyred,dt_k1_relat_1,dt_k1_rlvect_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k9_polynom1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,existence_l1_struct_0,existence_l2_struct_0,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc12_relat_1,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc17_polynom1,fc18_polynom1,fc19_polynom1,fc1_finsub_1,fc1_struct_0,fc20_polynom1,fc23_polynom1,fc24_polynom1,fc25_polynom1,fc2_finseq_1,fc3_polynom1,fc4_relat_1,fc5_polynom1,fc5_relat_1,fc7_relat_1,rc10_polynom1,rc11_polynom1,rc13_polynom1,rc1_finseq_1,rc1_finset_1,rc1_relat_1,rc1_rewrite1,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,rc8_polynom1,rc9_polynom1,redefinition_k14_polynom1,redefinition_k15_polynom1,redefinition_k4_relset_1,redefinition_m2_relset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r3_polynom1,reflexivity_r6_pboole,symmetry_r6_pboole,t1_subset,t1_termord,t2_subset,t39_polynom1,t3_subset,t40_polynom1,t4_subset,t51_polynom1,t52_polynom1,t5_subset,t6_boole,t7_boole,t8_boole,t9_funct_1]),
    [file(polyred,t18_polyred)]).

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_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_polynom1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => v1_polynom1(B) ) ) ),
    file(polynom1,cc6_polynom1),
    []).

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(commutativity_k9_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v1_seq_1(B)
        & m1_pboole(B,A)
        & v1_seq_1(C)
        & m1_pboole(C,A) )
     => k9_polynom1(A,B,C) = k9_polynom1(A,C,B) ) ),
    file(polynom1,k9_polynom1),
    []).

fof(d14_polynom1,axiom,(
    ! [A,B] : 
      ( B = k13_polynom1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) ) ) ) ),
    file(polynom1,d14_polynom1),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_polyred,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v7_seqm_3(B)
            & v1_polynom1(B)
            & m1_pboole(B,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))
                    & 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))
                        & m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
                     => ( E = k1_polyred(A,B,C,D)
                      <=> ! [F] : 
                            ( ( v7_seqm_3(F)
                              & v1_polynom1(F)
                              & m1_pboole(F,A) )
                           => ( r3_polynom1(A,B,F)
                             => ( k15_polynom1(A,C,E,F) = k15_polynom1(A,C,D,k10_polynom1(A,F,B))
                                & ! [G] : 
                                    ( ( v7_seqm_3(G)
                                      & v1_polynom1(G)
                                      & m1_pboole(G,A) )
                                   => ( ~ r3_polynom1(A,B,G)
                                     => k15_polynom1(A,C,E,G) = k1_rlvect_1(C) ) ) ) ) ) ) ) ) ) ) ) ),
    file(polyred,d1_polyred),
    []).

fof(dt_k10_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & m1_pboole(C,A) )
     => m1_pboole(k10_polynom1(A,B,C),A) ) ),
    file(polynom1,k10_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_k15_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(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))
        & v7_seqm_3(D)
        & v1_polynom1(D)
        & m1_pboole(D,A) )
     => m1_subset_1(k15_polynom1(A,B,C,D),u1_struct_0(B)) ) ),
    file(polynom1,k15_polynom1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_polyred,axiom,(
    ! [A,B,C,D] : 
      ( ( v3_ordinal1(A)
        & v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & ~ v3_struct_0(C)
        & l2_struct_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
        & m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
     => ( v1_funct_1(k1_polyred(A,B,C,D))
        & v1_funct_2(k1_polyred(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
        & m2_relset_1(k1_polyred(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) ) ) ),
    file(polyred,k1_polyred),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ),
    file(rlvect_1,k1_rlvect_1),
    []).

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_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k9_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v1_seq_1(B)
        & m1_pboole(B,A)
        & v1_seq_1(C)
        & m1_pboole(C,A) )
     => m1_pboole(k9_polynom1(A,B,C),A) ) ),
    file(polynom1,k9_polynom1),
    []).

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_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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_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_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    []).

fof(fc17_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v1_seq_1(B)
        & m1_pboole(B,A)
        & v1_seq_1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k9_polynom1(A,B,C))
        & v1_funct_1(k9_polynom1(A,B,C))
        & v1_seq_1(k9_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc17_polynom1),
    []).

fof(fc18_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k9_polynom1(A,B,C))
        & v1_funct_1(k9_polynom1(A,B,C))
        & v1_seq_1(k9_polynom1(A,B,C))
        & v7_seqm_3(k9_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc18_polynom1),
    []).

fof(fc19_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k10_polynom1(A,B,C))
        & v1_funct_1(k10_polynom1(A,B,C))
        & v1_seq_1(k10_polynom1(A,B,C))
        & v7_seqm_3(k10_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc19_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_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(fc23_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k9_polynom1(A,B,C))
        & v1_funct_1(k9_polynom1(A,B,C))
        & v1_seq_1(k9_polynom1(A,B,C))
        & v7_seqm_3(k9_polynom1(A,B,C))
        & v1_polynom1(k9_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc23_polynom1),
    []).

fof(fc24_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => ( v1_relat_1(k10_polynom1(A,B,C))
        & v1_funct_1(k10_polynom1(A,B,C))
        & v1_seq_1(k10_polynom1(A,B,C))
        & v7_seqm_3(k10_polynom1(A,B,C))
        & v1_polynom1(k10_polynom1(A,B,C)) ) ) ),
    file(polynom1,fc24_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(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(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc5_polynom1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_matrlin(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B))
        & v1_finset_1(k1_funct_1(A,B))
        & v1_finseq_1(k1_funct_1(A,B)) ) ) ),
    file(polynom1,fc5_polynom1),
    []).

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(rc10_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B) ) ),
    file(polynom1,rc10_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(rc13_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B)
      & v7_seqm_3(B)
      & v1_polynom1(B) ) ),
    file(polynom1,rc13_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_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_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(rc8_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B)
      & v7_seqm_3(B) ) ),
    file(polynom1,rc8_polynom1),
    []).

fof(rc9_polynom1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_seq_1(B) ) ),
    file(polynom1,rc9_polynom1),
    []).

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

fof(redefinition_k15_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(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))
        & v7_seqm_3(D)
        & v1_polynom1(D)
        & m1_pboole(D,A) )
     => k15_polynom1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(polynom1,k15_polynom1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

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(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

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

fof(reflexivity_r3_polynom1,axiom,(
    ! [A,B,C] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A)
        & v7_seqm_3(C)
        & v1_polynom1(C)
        & m1_pboole(C,A) )
     => r3_polynom1(A,B,B) ) ),
    file(polynom1,r3_polynom1),
    []).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

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

fof(t1_termord,axiom,(
    ! [A,B] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) )
         => ( r3_polynom1(A,B,C)
          <=> ? [D] : 
                ( v7_seqm_3(D)
                & v1_polynom1(D)
                & m1_pboole(D,A)
                & r6_pboole(A,C,k9_polynom1(A,B,D)) ) ) ) ) ),
    file(termord,t1_termord),
    []).

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

fof(t39_polynom1,axiom,(
    ! [A,B] : 
      ( ( v1_seq_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_seq_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( ( v1_seq_1(D)
                & m1_pboole(D,A) )
             => r6_pboole(A,k9_polynom1(A,k9_polynom1(A,B,C),D),k9_polynom1(A,B,k9_polynom1(A,C,D))) ) ) ) ),
    file(polynom1,t39_polynom1),
    []).

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

fof(t40_polynom1,axiom,(
    ! [A,B] : 
      ( ( v7_seqm_3(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v7_seqm_3(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( ( v7_seqm_3(D)
                & m1_pboole(D,A) )
             => r6_pboole(A,k10_polynom1(A,k10_polynom1(A,B,C),D),k10_polynom1(A,B,k9_polynom1(A,C,D))) ) ) ) ),
    file(polynom1,t40_polynom1),
    []).

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(t51_polynom1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v7_seqm_3(B)
            & v1_polynom1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( ( v7_seqm_3(C)
                & v1_polynom1(C)
                & m1_pboole(C,A) )
             => ( r3_polynom1(A,B,C)
               => r6_pboole(A,k9_polynom1(A,k10_polynom1(A,C,B),B),C) ) ) ) ) ),
    file(polynom1,t51_polynom1),
    []).

fof(t52_polynom1,axiom,(
    ! [A,B] : 
      ( ( v7_seqm_3(B)
        & v1_polynom1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v7_seqm_3(C)
            & v1_polynom1(C)
            & m1_pboole(C,A) )
         => r6_pboole(A,k10_polynom1(A,k9_polynom1(A,C,B),B),C) ) ) ),
    file(polynom1,t52_polynom1),
    []).

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),
    []).

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).