% Mizar problem: t18_pencil_3,pencil_3,745,69 
fof(t18_pencil_3,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v15_pencil_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( ( ~ v13_pencil_1(C)
                & v16_pencil_1(C,A)
                & m4_pboole(C,A,k12_pralg_1(A,B)) )
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k2_pencil_1(A,B,k3_pencil_1(A,C))))
                 => ? [E] : 
                      ( m1_pboole(E,A)
                      & r2_hidden(E,k4_card_3(C))
                      & k1_tarski(k2_polynom1(A,E,k3_pencil_1(A,C),D)) = k4_card_3(k2_polynom1(A,C,k3_pencil_1(A,C),k1_struct_0(k2_pencil_1(A,B,k3_pencil_1(A,C)),D))) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_pboole,cc1_pencil_1,cc1_realset1,cc2_finset_1,cc2_pboole,cc2_pencil_1,cc3_pencil_1,cc4_pencil_1,cc5_pencil_1,cc6_pencil_1,d10_xboole_0,d1_tarski,d1_xboole_0,d21_pencil_1,d3_pboole,d3_tarski,d4_realset1,d5_card_3,dt_k12_pralg_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funct_7,dt_k2_pencil_1,dt_k2_polynom1,dt_k3_pencil_1,dt_k4_card_3,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pboole,dt_m1_subset_1,dt_m4_pboole,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pboole,existence_m1_subset_1,existence_m4_pboole,fc1_finset_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_pboole,fc2_subset_1,fc3_realset1,fc4_pencil_1,rc1_finset_1,rc1_pboole,rc1_realset1,rc1_subset_1,rc1_xboole_0,rc2_pboole,rc2_realset1,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc3_pboole,rc3_pencil_1,rc3_struct_0,rc4_finset_1,rc4_pencil_1,rc5_pboole,rc5_pencil_1,rc5_struct_0,rc6_pencil_1,rc7_pencil_1,rc8_pencil_1,redefinition_k1_struct_0,redefinition_k2_pencil_1,redefinition_k2_polynom1,reflexivity_r1_tarski,t18_card_3,t1_subset,t2_subset,t33_funct_7,t34_funct_7,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t9_funct_1]),
    [file(pencil_3,t18_pencil_3)]).

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

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

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

fof(cc1_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v11_pencil_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) ),
    file(pencil_1,cc1_pencil_1),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

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_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(cc2_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v14_pencil_1(A) )
     => ( v1_relat_1(A)
        & v4_waybel_3(A) ) ) ),
    file(pencil_1,cc2_pencil_1),
    []).

fof(cc3_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v15_pencil_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_waybel_3(A)
        & v2_pralg_1(A)
        & v11_pencil_1(A) ) ) ),
    file(pencil_1,cc3_pencil_1),
    []).

fof(cc4_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v11_pencil_1(A)
        & v15_pencil_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A)
        & v11_pencil_1(A)
        & v12_pencil_1(A) ) ) ),
    file(pencil_1,cc4_pencil_1),
    []).

fof(cc5_pencil_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v11_pencil_1(A)
        & v15_pencil_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_waybel_3(A)
        & v2_pralg_1(A)
        & v11_pencil_1(A)
        & v14_pencil_1(A) ) ) ),
    file(pencil_1,cc5_pencil_1),
    []).

fof(cc6_pencil_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( ( ~ v13_pencil_1(B)
              & v16_pencil_1(B,A) )
           => v2_relat_1(B) ) ) ) ),
    file(pencil_1,cc6_pencil_1),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

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

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d21_pencil_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v13_pencil_1(B)
            & v16_pencil_1(B,A)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ( C = k3_pencil_1(A,B)
              <=> ~ v1_realset1(k1_funct_1(B,C)) ) ) ) ) ),
    file(pencil_1,d21_pencil_1),
    []).

fof(d3_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d4_realset1,axiom,(
    ! [A] : 
      ( v1_realset1(A)
    <=> ~ ( ~ v1_xboole_0(A)
          & ! [B] : A != k1_tarski(B) ) ) ),
    file(realset1,d4_realset1),
    []).

fof(d5_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    []).

fof(dt_k12_pralg_1,axiom,(
    ! [A,B] : 
      ( ( v2_pralg_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k12_pralg_1(A,B),A) ) ),
    file(pralg_1,k12_pralg_1),
    []).

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

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

fof(dt_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    []).

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

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_funct_7,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_7(A,B,C))
        & v1_funct_1(k2_funct_7(A,B,C)) ) ) ),
    file(funct_7,k2_funct_7),
    []).

fof(dt_k2_pencil_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v15_pencil_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(k2_pencil_1(A,B,C))
        & ~ v3_pencil_1(k2_pencil_1(A,B,C))
        & ~ v4_pencil_1(k2_pencil_1(A,B,C))
        & v5_pencil_1(k2_pencil_1(A,B,C))
        & v6_pencil_1(k2_pencil_1(A,B,C))
        & l1_pre_topc(k2_pencil_1(A,B,C)) ) ) ),
    file(pencil_1,k2_pencil_1),
    []).

fof(dt_k2_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( m1_pboole(B,A)
     => m1_pboole(k2_polynom1(A,B,C,D),A) ) ),
    file(polynom1,k2_polynom1),
    []).

fof(dt_k3_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v13_pencil_1(B)
        & v16_pencil_1(B,A)
        & m1_pboole(B,A) )
     => m1_subset_1(k3_pencil_1(A,B),A) ) ),
    file(pencil_1,k3_pencil_1),
    []).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pboole,m4_pboole),
    []).

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

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

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

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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

fof(existence_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : m4_pboole(C,A,B) ) ),
    file(pboole,m4_pboole),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_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(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(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

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

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc4_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v13_pencil_1(B)
        & v16_pencil_1(B,A)
        & m1_pboole(B,A) )
     => ( ~ v1_xboole_0(k4_card_3(B))
        & v1_fraenkel(k4_card_3(B))
        & ~ v1_realset1(k4_card_3(B)) ) ) ),
    file(pencil_1,fc4_pencil_1),
    []).

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

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

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_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

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(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_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc3_pencil_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v11_pencil_1(B) ) ),
    file(pencil_1,rc3_pencil_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_pencil_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_pralg_1(A)
      & v11_pencil_1(A) ) ),
    file(pencil_1,rc4_pencil_1),
    []).

fof(rc5_pboole,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(pboole,rc5_pboole),
    []).

fof(rc5_pencil_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v4_waybel_3(B)
      & v2_pralg_1(B)
      & v11_pencil_1(B)
      & v12_pencil_1(B)
      & v14_pencil_1(B)
      & v15_pencil_1(B) ) ),
    file(pencil_1,rc5_pencil_1),
    []).

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_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v2_pralg_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,k12_pralg_1(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C)
          & v13_pencil_1(C)
          & v16_pencil_1(C,A) ) ) ),
    file(pencil_1,rc6_pencil_1),
    []).

fof(rc7_pencil_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v2_pralg_1(B)
        & v14_pencil_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,k12_pralg_1(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C)
          & ~ v13_pencil_1(C)
          & v16_pencil_1(C,A) ) ) ),
    file(pencil_1,rc7_pencil_1),
    []).

fof(rc8_pencil_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & ~ v13_pencil_1(B)
          & v16_pencil_1(B,A) ) ) ),
    file(pencil_1,rc8_pencil_1),
    []).

fof(redefinition_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(redefinition_k2_pencil_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v15_pencil_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k2_pencil_1(A,B,C) = k1_funct_1(B,C) ) ),
    file(pencil_1,k2_pencil_1),
    []).

fof(redefinition_k2_polynom1,axiom,(
    ! [A,B,C,D] : 
      ( m1_pboole(B,A)
     => k2_polynom1(A,B,C,D) = k2_funct_7(B,C,D) ) ),
    file(polynom1,k2_polynom1),
    []).

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

fof(t18_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    []).

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(t33_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( r2_hidden(C,k1_relat_1(A))
         => k1_funct_1(k2_funct_7(A,C,B),C) = B ) ) ),
    file(funct_7,t33_funct_7),
    []).

fof(t34_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D] : 
          ( C != D
         => k1_funct_1(k2_funct_7(A,C,B),D) = k1_funct_1(A,D) ) ) ),
    file(funct_7,t34_funct_7),
    []).

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),
    []).

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),
    []).