% Mizar problem: t19_trees_a,trees_a,893,40 
fof(t19_trees_a,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(A))
             => k3_trees_a(A,k2_trees_a(k1_relat_1(A),C),B) = k8_trees_2(A,C,B) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,commutativity_k2_xboole_0,d12_trees_2,d1_tarski,d2_trees_a,d2_xboole_0,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_trees_a,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_trees_a,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_trees_a,dt_k5_numbers,dt_k5_ordinal2,dt_k5_trees_1,dt_k7_finseq_1,dt_k8_finseq_1,dt_k8_trees_2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m4_trees_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m4_trees_1,fc10_membered,fc11_membered,fc1_subset_1,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_membered,fc2_subset_1,fc2_trees_2,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,fc5_membered,fc6_membered,fc7_membered,fc8_membered,fc9_membered,fraenkel_a_2_1_trees_a,fraenkel_a_2_2_trees_a,fraenkel_a_2_3_trees_a,fraenkel_a_2_4_trees_a,fraenkel_a_2_5_trees_a,fraenkel_a_2_6_trees_a,fraenkel_a_3_0_trees_a,fraenkel_a_3_2_trees_a,fraenkel_a_3_3_trees_a,fraenkel_a_3_4_trees_a,idempotence_k2_xboole_0,rc1_arytm_3,rc1_membered,rc1_subset_1,rc1_trees_a,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc5_trees_2,rc9_trees_2,redefinition_k2_trees_a,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,reflexivity_r1_tarski,t10_trees_a,t15_trees_a,t16_trees_a,t17_trees_a,t18_trees_a,t1_boole,t1_subset,t2_subset,t2_tarski,t33_trees_2,t3_subset,t46_finseq_1,t4_subset,t5_subset,t6_boole,t7_boole,t7_trees_a,t8_boole]),
    [file(trees_a,t19_trees_a)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

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(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d12_trees_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v3_trees_2(C) )
             => ( r2_hidden(B,k1_relat_1(A))
               => ! [D] : 
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & v3_trees_2(D) )
                   => ( D = k8_trees_2(A,B,C)
                    <=> ( k1_relat_1(D) = k5_trees_1(k1_relat_1(A),B,k1_relat_1(C))
                        & ! [E] : 
                            ( m2_finseq_1(E,k5_numbers)
                           => ~ ( r2_hidden(E,k5_trees_1(k1_relat_1(A),B,k1_relat_1(C)))
                                & ~ ( ~ r1_tarski(B,E)
                                    & k1_funct_1(D,E) = k1_funct_1(A,E) )
                                & ! [F] : 
                                    ( m2_finseq_1(F,k5_numbers)
                                   => ~ ( r2_hidden(F,k1_relat_1(C))
                                        & E = k8_finseq_1(k5_numbers,B,F)
                                        & k1_funct_1(D,E) = k1_funct_1(C,F) ) ) ) ) ) ) ) ) ) ) ) ),
    file(trees_2,d12_trees_2),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d2_trees_a,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( m4_trees_1(B,k1_relat_1(A))
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v3_trees_2(C) )
             => ( B != k1_xboole_0
               => ! [D] : 
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & v3_trees_2(D) )
                   => ( D = k3_trees_a(A,B,C)
                    <=> ( k1_relat_1(D) = k1_trees_a(k1_relat_1(A),k1_relat_1(C),B)
                        & ! [E] : 
                            ( m2_finseq_1(E,k5_numbers)
                           => ~ ( r2_hidden(E,k1_trees_a(k1_relat_1(A),k1_relat_1(C),B))
                                & ? [F] : 
                                    ( m2_finseq_1(F,k5_numbers)
                                    & r2_hidden(F,B)
                                    & ~ ( ~ r1_tarski(F,E)
                                        & k1_funct_1(D,E) = k1_funct_1(A,E) ) )
                                & ! [F] : 
                                    ( m2_finseq_1(F,k5_numbers)
                                   => ! [G] : 
                                        ( m2_finseq_1(G,k5_numbers)
                                       => ~ ( r2_hidden(F,B)
                                            & r2_hidden(G,k1_relat_1(C))
                                            & E = k8_finseq_1(k5_numbers,F,G)
                                            & k1_funct_1(D,E) = k1_funct_1(C,G) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(trees_a,d2_trees_a),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

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

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_trees_a,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_trees_1(B)
        & m4_trees_1(C,A) )
     => ( ~ v1_xboole_0(k1_trees_a(A,B,C))
        & v1_trees_1(k1_trees_a(A,B,C)) ) ) ),
    file(trees_a,k1_trees_a),
    []).

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_trees_a,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & m1_subset_1(B,A) )
     => ( ~ v1_xboole_0(k2_trees_a(A,B))
        & m4_trees_1(k2_trees_a(A,B),A) ) ) ),
    file(trees_a,k2_trees_a),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_trees_a,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & m4_trees_1(B,k1_relat_1(A))
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v3_trees_2(C) )
     => ( v1_relat_1(k3_trees_a(A,B,C))
        & v1_funct_1(k3_trees_a(A,B,C))
        & v3_trees_2(k3_trees_a(A,B,C)) ) ) ),
    file(trees_a,k3_trees_a),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_trees_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & m1_finseq_1(B,k5_numbers)
        & ~ v1_xboole_0(C)
        & v1_trees_1(C) )
     => ( ~ v1_xboole_0(k5_trees_1(A,B,C))
        & v1_trees_1(k5_trees_1(A,B,C)) ) ) ),
    file(trees_1,k5_trees_1),
    []).

fof(dt_k7_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B)) ) ) ),
    file(finseq_1,k7_finseq_1),
    []).

fof(dt_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ),
    file(finseq_1,k8_finseq_1),
    []).

fof(dt_k8_trees_2,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & m1_finseq_1(B,k5_numbers)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v3_trees_2(C) )
     => ( v1_relat_1(k8_trees_2(A,B,C))
        & v1_funct_1(k8_trees_2(A,B,C))
        & v3_trees_2(k8_trees_2(A,B,C)) ) ) ),
    file(trees_2,k8_trees_2),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_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_m1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => m2_finseq_1(B,k5_numbers) ) ) ),
    file(trees_1,m1_trees_1),
    []).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_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_m4_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m4_trees_1(B,A)
         => v2_trees_1(B) ) ) ),
    file(trees_1,m4_trees_1),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_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_m1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : m1_trees_1(B,A) ) ),
    file(trees_1,m1_trees_1),
    []).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

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

fof(existence_m4_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : m4_trees_1(B,A) ) ),
    file(trees_1,m4_trees_1),
    []).

fof(fc10_membered,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    []).

fof(fc11_membered,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc22_membered,axiom,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    []).

fof(fc23_membered,axiom,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    []).

fof(fc24_membered,axiom,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    []).

fof(fc25_membered,axiom,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    []).

fof(fc26_membered,axiom,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_trees_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ( ~ v1_xboole_0(k1_relat_1(A))
        & v1_trees_1(k1_relat_1(A)) ) ) ),
    file(trees_2,fc2_trees_2),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(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) ),
    file(membered,fc6_membered),
    []).

fof(fc7_membered,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    []).

fof(fc8_membered,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    []).

fof(fc9_membered,axiom,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    []).

fof(fraenkel_a_2_1_trees_a,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & v1_trees_1(B)
        & m4_trees_1(C,B) )
     => ( r2_hidden(A,a_2_1_trees_a(B,C))
      <=> ? [D] : 
            ( m1_trees_1(D,B)
            & A = D
            & ! [E] : 
                ( m2_finseq_1(E,k5_numbers)
               => ~ ( r2_hidden(E,C)
                    & r1_tarski(E,D) ) ) ) ) ) ),
    file(trees_a,a_2_1_trees_a),
    []).

fof(fraenkel_a_2_2_trees_a,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & m4_trees_1(C,k1_relat_1(B)) )
     => ( r2_hidden(A,a_2_2_trees_a(B,C))
      <=> ? [D] : 
            ( m1_trees_1(D,k1_relat_1(B))
            & A = D
            & ! [E] : 
                ( m2_finseq_1(E,k5_numbers)
               => ~ ( r2_hidden(E,C)
                    & r1_tarski(E,D) ) ) ) ) ) ),
    file(trees_a,a_2_2_trees_a),
    []).

fof(fraenkel_a_2_3_trees_a,axiom,(
    ! [A,B,C] : 
      ( ( m2_finseq_1(B,k5_numbers)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v3_trees_2(C) )
     => ( r2_hidden(A,a_2_3_trees_a(B,C))
      <=> ? [D] : 
            ( m1_trees_1(D,k1_relat_1(C))
            & A = D
            & ~ r1_tarski(B,D) ) ) ) ),
    file(trees_a,a_2_3_trees_a),
    []).

fof(fraenkel_a_2_4_trees_a,axiom,(
    ! [A,B,C] : 
      ( ( m2_finseq_1(B,k5_numbers)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v3_trees_2(C) )
     => ( r2_hidden(A,a_2_4_trees_a(B,C))
      <=> ? [D] : 
            ( m1_trees_1(D,k1_relat_1(C))
            & A = k8_finseq_1(k5_numbers,B,D)
            & D = D ) ) ) ),
    file(trees_a,a_2_4_trees_a),
    []).

fof(fraenkel_a_2_5_trees_a,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & m1_trees_1(C,k1_relat_1(B)) )
     => ( r2_hidden(A,a_2_5_trees_a(B,C))
      <=> ? [D] : 
            ( m1_trees_1(D,k1_relat_1(B))
            & A = D
            & ! [E] : 
                ( m2_finseq_1(E,k5_numbers)
               => ~ ( r2_hidden(E,k2_trees_a(k1_relat_1(B),C))
                    & r1_tarski(E,D) ) ) ) ) ) ),
    file(trees_a,a_2_5_trees_a),
    []).

fof(fraenkel_a_2_6_trees_a,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & m2_finseq_1(C,k5_numbers) )
     => ( r2_hidden(A,a_2_6_trees_a(B,C))
      <=> ? [D] : 
            ( m1_trees_1(D,k1_relat_1(B))
            & A = D
            & ~ r1_tarski(C,D) ) ) ) ),
    file(trees_a,a_2_6_trees_a),
    []).

fof(fraenkel_a_3_0_trees_a,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_trees_1(B)
        & ~ v1_xboole_0(C)
        & v1_trees_1(C)
        & m4_trees_1(D,B) )
     => ( r2_hidden(A,a_3_0_trees_a(B,C,D))
      <=> ? [E,F] : 
            ( m1_trees_1(E,B)
            & m1_trees_1(F,C)
            & A = k8_finseq_1(k5_numbers,E,F)
            & r2_hidden(E,D) ) ) ) ),
    file(trees_a,a_3_0_trees_a),
    []).

fof(fraenkel_a_3_2_trees_a,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m4_trees_1(D,k1_relat_1(B)) )
     => ( r2_hidden(A,a_3_2_trees_a(B,C,D))
      <=> ? [E,F] : 
            ( m1_trees_1(E,k1_relat_1(B))
            & m1_trees_1(F,k1_relat_1(C))
            & A = k8_finseq_1(k5_numbers,E,F)
            & r2_hidden(E,D) ) ) ) ),
    file(trees_a,a_3_2_trees_a),
    []).

fof(fraenkel_a_3_3_trees_a,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m1_trees_1(D,k1_relat_1(B)) )
     => ( r2_hidden(A,a_3_3_trees_a(B,C,D))
      <=> ? [E,F] : 
            ( m1_trees_1(E,k1_relat_1(B))
            & m1_trees_1(F,k1_relat_1(C))
            & A = k8_finseq_1(k5_numbers,E,F)
            & r2_hidden(E,k2_trees_a(k1_relat_1(B),D)) ) ) ) ),
    file(trees_a,a_3_3_trees_a),
    []).

fof(fraenkel_a_3_4_trees_a,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & v1_relat_1(C)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m1_trees_1(D,k1_relat_1(B)) )
     => ( r2_hidden(A,a_3_4_trees_a(B,C,D))
      <=> ? [E] : 
            ( m1_trees_1(E,k1_relat_1(C))
            & A = k8_finseq_1(k5_numbers,D,E)
            & E = E ) ) ) ),
    file(trees_a,a_3_4_trees_a),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_trees_a,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ? [B] : 
          ( m4_trees_1(B,A)
          & ~ v1_xboole_0(B)
          & v2_trees_1(B) ) ) ),
    file(trees_a,rc1_trees_a),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc5_trees_2,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v3_trees_2(A) ) ),
    file(trees_2,rc5_trees_2),
    []).

fof(rc9_trees_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ? [C] : 
          ( m1_relset_1(C,A,B)
          & v1_relat_1(C)
          & ~ v1_xboole_0(C) ) ) ),
    file(trees_2,rc9_trees_2),
    []).

fof(redefinition_k2_trees_a,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & m1_subset_1(B,A) )
     => k2_trees_a(A,B) = k1_tarski(B) ) ),
    file(trees_a,k2_trees_a),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k8_finseq_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_finseq_1(B,A)
        & m1_finseq_1(C,A) )
     => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ),
    file(finseq_1,k8_finseq_1),
    []).

fof(redefinition_m1_trees_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
        <=> m1_subset_1(B,A) ) ) ),
    file(trees_1,m1_trees_1),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t10_trees_a,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( m1_trees_1(C,A)
             => k1_trees_a(A,B,k2_trees_a(A,C)) = k5_trees_1(A,C,B) ) ) ) ),
    file(trees_a,t10_trees_a),
    []).

fof(t15_trees_a,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( m4_trees_1(C,k1_relat_1(A))
             => ( C != k1_xboole_0
               => ! [D] : 
                    ( m2_finseq_1(D,k5_numbers)
                   => ( ( r2_hidden(D,k1_relat_1(k3_trees_a(A,C,B)))
                        & r2_hidden(D,a_2_2_trees_a(A,C)) )
                     => k1_funct_1(k3_trees_a(A,C,B),D) = k1_funct_1(A,D) ) ) ) ) ) ) ),
    file(trees_a,t15_trees_a),
    []).

fof(t16_trees_a,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v3_trees_2(C) )
             => ( r2_hidden(A,k1_relat_1(B))
               => ! [D] : 
                    ( m2_finseq_1(D,k5_numbers)
                   => ( ( r2_hidden(D,k1_relat_1(k8_trees_2(B,A,C)))
                        & r2_hidden(D,a_2_3_trees_a(A,B)) )
                     => k1_funct_1(k8_trees_2(B,A,C),D) = k1_funct_1(B,D) ) ) ) ) ) ) ),
    file(trees_a,t16_trees_a),
    []).

fof(t17_trees_a,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( m4_trees_1(C,k1_relat_1(A))
             => ! [D] : 
                  ( m2_finseq_1(D,k5_numbers)
                 => ~ ( r2_hidden(D,k1_relat_1(k3_trees_a(A,C,B)))
                      & r2_hidden(D,a_3_2_trees_a(A,B,C))
                      & ! [E] : 
                          ( m1_trees_1(E,k1_relat_1(A))
                         => ! [F] : 
                              ( m1_trees_1(F,k1_relat_1(B))
                             => ~ ( D = k8_finseq_1(k5_numbers,E,F)
                                  & r2_hidden(E,C)
                                  & k1_funct_1(k3_trees_a(A,C,B),D) = k1_funct_1(B,F) ) ) ) ) ) ) ) ) ),
    file(trees_a,t17_trees_a),
    []).

fof(t18_trees_a,axiom,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v3_trees_2(C) )
             => ( r2_hidden(A,k1_relat_1(B))
               => ! [D] : 
                    ( m2_finseq_1(D,k5_numbers)
                   => ~ ( r2_hidden(D,k1_relat_1(k8_trees_2(B,A,C)))
                        & r2_hidden(D,a_2_4_trees_a(A,C))
                        & ! [E] : 
                            ( m1_trees_1(E,k1_relat_1(C))
                           => ~ ( D = k8_finseq_1(k5_numbers,A,E)
                                & k1_funct_1(k8_trees_2(B,A,C),D) = k1_funct_1(C,E) ) ) ) ) ) ) ) ) ),
    file(trees_a,t18_trees_a),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t33_trees_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( m2_finseq_1(C,k5_numbers)
                 => ( r2_hidden(C,k1_relat_1(A))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(trees_2,t33_trees_2),
    []).

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

fof(t46_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k7_finseq_1(A,B) = k7_finseq_1(C,B)
                  | k7_finseq_1(B,A) = k7_finseq_1(B,C) )
               => A = C ) ) ) ) ),
    file(finseq_1,t46_finseq_1),
    []).

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(t7_trees_a,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( m4_trees_1(C,A)
             => ( C != k1_xboole_0
               => k1_trees_a(A,B,C) = k2_xboole_0(a_2_1_trees_a(A,C),a_3_0_trees_a(A,B,C)) ) ) ) ) ),
    file(trees_a,t7_trees_a),
    []).

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