% Mizar problem: t9_arytm_2,arytm_2,1425,51 
fof(t9_arytm_2,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k2_arytm_2))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k2_arytm_2))
         => ~ ( ? [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                  & r2_hidden(C,A) )
              & ? [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                  & r2_hidden(C,B) )
              & ! [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                 => ! [D] : 
                      ( m1_subset_1(D,k2_arytm_2)
                     => ( ( r2_hidden(C,A)
                          & r2_hidden(D,B) )
                       => r1_arytm_2(C,D) ) ) )
              & ! [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                 => ? [D] : 
                      ( m1_subset_1(D,k2_arytm_2)
                      & ? [E] : 
                          ( m1_subset_1(E,k2_arytm_2)
                          & r2_hidden(D,A)
                          & r2_hidden(E,B)
                          & ~ ( r1_arytm_2(D,C)
                              & r1_arytm_2(C,E) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_ordinal1,cc4_arytm_3,commutativity_k2_xboole_0,commutativity_k3_xboole_0,connectedness_r1_arytm_2,connectedness_r3_arytm_3,d1_arytm_2,d1_tarski,d2_arytm_2,d2_xboole_0,d3_tarski,d3_xboole_0,d4_xboole_0,d5_arytm_2,dt_k12_arytm_3,dt_k1_arytm_2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k2_xboole_0,dt_k3_xboole_0,dt_k4_xboole_0,dt_k6_arytm_3,dt_m1_subset_1,existence_m1_subset_1,fc1_arytm_2,fc1_subset_1,fc1_xboole_0,fc2_arytm_2,fc2_ordinal1,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc8_arytm_3,fraenkel_a_0_0_arytm_2,fraenkel_a_0_2_arytm_2,fraenkel_a_1_0_arytm_2,fraenkel_a_1_1_arytm_2,idempotence_k2_xboole_0,idempotence_k3_xboole_0,l10_arytm_2,l12_arytm_2,l20_arytm_2,l26_arytm_2,l49_arytm_2,l51_arytm_2,l52_arytm_2,rc1_arytm_3,rc1_ordinal1,rc1_subset_1,rc1_xboole_0,rc2_arytm_3,rc2_ordinal1,rc2_subset_1,rc2_xboole_0,rc3_arytm_3,rc3_ordinal1,redefinition_k12_arytm_3,reflexivity_r1_tarski,t1_arytm_2,t1_boole,t1_subset,t2_boole,t2_subset,t2_tarski,t3_boole,t3_subset,t49_subset_1,t4_boole,t4_subset,t5_subset,t64_zfmisc_1,t6_boole,t71_arytm_3,t7_boole,t8_boole]),
    [file(arytm_2,t9_arytm_2)]).

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

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_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

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_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

fof(cc4_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ( v3_ordinal1(A)
       => ( v1_ordinal1(A)
          & v2_ordinal1(A)
          & v3_ordinal1(A)
          & v4_ordinal2(A) ) ) ) ),
    file(arytm_3,cc4_arytm_3),
    []).

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(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(connectedness_r1_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => ( r1_arytm_2(A,B)
        | r1_arytm_2(B,A) ) ) ),
    file(arytm_2,r1_arytm_2),
    []).

fof(connectedness_r3_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => ( r3_arytm_3(A,B)
        | r3_arytm_3(B,A) ) ) ),
    file(arytm_3,r3_arytm_3),
    []).

fof(d1_arytm_2,axiom,(
    k1_arytm_2 = k4_xboole_0(a_0_0_arytm_2,k1_tarski(k6_arytm_3)) ),
    file(arytm_2,d1_arytm_2),
    []).

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

fof(d2_arytm_2,axiom,(
    k2_arytm_2 = k4_xboole_0(k2_xboole_0(k6_arytm_3,k1_arytm_2),a_0_2_arytm_2) ),
    file(arytm_2,d2_arytm_2),
    []).

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

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( ( r2_hidden(A,k6_arytm_3)
                & r2_hidden(B,k6_arytm_3) )
             => ( r1_arytm_2(A,B)
              <=> ? [C] : 
                    ( m1_subset_1(C,k6_arytm_3)
                    & ? [D] : 
                        ( m1_subset_1(D,k6_arytm_3)
                        & A = C
                        & B = D
                        & r3_arytm_3(C,D) ) ) ) )
            & ( r2_hidden(A,k6_arytm_3)
             => ( r2_hidden(B,k6_arytm_3)
                | ( r1_arytm_2(A,B)
                <=> r2_hidden(A,B) ) ) )
            & ( r2_hidden(B,k6_arytm_3)
             => ( r2_hidden(A,k6_arytm_3)
                | ( r1_arytm_2(A,B)
                <=> ~ r2_hidden(B,A) ) ) )
            & ~ ( ~ ( r2_hidden(A,k6_arytm_3)
                    & r2_hidden(B,k6_arytm_3) )
                & ~ ( r2_hidden(A,k6_arytm_3)
                    & ~ r2_hidden(B,k6_arytm_3) )
                & ~ ( ~ r2_hidden(A,k6_arytm_3)
                    & r2_hidden(B,k6_arytm_3) )
                & ~ ( r1_arytm_2(A,B)
                  <=> r1_tarski(A,B) ) ) ) ) ) ),
    file(arytm_2,d5_arytm_2),
    []).

fof(dt_k12_arytm_3,axiom,
    ( v1_xboole_0(k12_arytm_3)
    & m1_subset_1(k12_arytm_3,k6_arytm_3) ),
    file(arytm_3,k12_arytm_3),
    []).

fof(dt_k1_arytm_2,axiom,(
    m1_subset_1(k1_arytm_2,k1_zfmisc_1(k1_zfmisc_1(k6_arytm_3))) ),
    file(arytm_2,k1_arytm_2),
    []).

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_arytm_2,axiom,(
    $true ),
    file(arytm_2,k2_arytm_2),
    []).

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

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k6_arytm_3,axiom,(
    $true ),
    file(arytm_3,k6_arytm_3),
    []).

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

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

fof(fc1_arytm_2,axiom,(
    ~ v1_xboole_0(k1_arytm_2) ),
    file(arytm_2,fc1_arytm_2),
    []).

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_arytm_2,axiom,(
    ~ v1_xboole_0(k2_arytm_2) ),
    file(arytm_2,fc2_arytm_2),
    []).

fof(fc2_ordinal1,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_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

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

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(fc8_arytm_3,axiom,(
    ~ v1_xboole_0(k6_arytm_3) ),
    file(arytm_3,fc8_arytm_3),
    []).

fof(fraenkel_a_0_0_arytm_2,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_arytm_2)
    <=> ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k6_arytm_3))
          & A = B
          & ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( r2_hidden(C,B)
               => ( ! [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                     => ( r3_arytm_3(D,C)
                       => r2_hidden(D,B) ) )
                  & ? [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                      & r2_hidden(D,B)
                      & ~ r3_arytm_3(D,C) ) ) ) ) ) ) ),
    file(arytm_2,a_0_0_arytm_2),
    []).

fof(fraenkel_a_0_2_arytm_2,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_2_arytm_2)
    <=> ? [B] : 
          ( m1_subset_1(B,k6_arytm_3)
          & A = a_1_0_arytm_2(B)
          & B != k12_arytm_3 ) ) ),
    file(arytm_2,a_0_2_arytm_2),
    []).

fof(fraenkel_a_1_0_arytm_2,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k6_arytm_3)
     => ( r2_hidden(A,a_1_0_arytm_2(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k6_arytm_3)
            & A = C
            & ~ r3_arytm_3(B,C) ) ) ) ),
    file(arytm_2,a_1_0_arytm_2),
    []).

fof(fraenkel_a_1_1_arytm_2,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k2_arytm_2))
     => ( r2_hidden(A,a_1_1_arytm_2(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k6_arytm_3)
            & A = C
            & ? [D] : 
                ( m1_subset_1(D,k2_arytm_2)
                & ? [E] : 
                    ( m1_subset_1(E,k2_arytm_2)
                    & E = C
                    & r2_hidden(D,B)
                    & ~ r1_arytm_2(D,E) ) ) ) ) ) ),
    file(arytm_2,a_1_1_arytm_2),
    []).

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

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(l10_arytm_2,axiom,(
    r1_tarski(k2_arytm_2,k2_xboole_0(k6_arytm_3,a_0_0_arytm_2)) ),
    file(arytm_2,l10_arytm_2),
    []).

fof(l12_arytm_2,axiom,(
    r1_tarski(k4_xboole_0(k1_arytm_2,a_0_2_arytm_2),k2_arytm_2) ),
    file(arytm_2,l12_arytm_2),
    []).

fof(l20_arytm_2,axiom,(
    k3_xboole_0(k1_arytm_2,k6_arytm_3) = k1_tarski(k12_arytm_3) ),
    file(arytm_2,l20_arytm_2),
    []).

fof(l26_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => ! [D] : 
                  ( m1_subset_1(D,k2_arytm_2)
                 => ( ( C = A
                      & D = B )
                   => ( r1_arytm_2(C,D)
                    <=> r3_arytm_3(A,B) ) ) ) ) ) ) ),
    file(arytm_2,l26_arytm_2),
    []).

fof(l49_arytm_2,axiom,(
    ! [A] : ~ ( r2_hidden(A,k2_arytm_2)
      & A = k6_arytm_3 ) ),
    file(arytm_2,l49_arytm_2),
    []).

fof(l51_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ~ ( ~ r1_arytm_2(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                 => ~ ( r2_hidden(C,k6_arytm_3)
                      & ~ r1_arytm_2(B,C)
                      & ~ r1_arytm_2(C,A) ) ) ) ) ) ),
    file(arytm_2,l51_arytm_2),
    []).

fof(l52_arytm_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => ( ( r1_arytm_2(A,B)
                  & r1_arytm_2(B,C) )
               => r1_arytm_2(A,C) ) ) ) ) ),
    file(arytm_2,l52_arytm_2),
    []).

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_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

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_arytm_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(arytm_3,rc2_arytm_3),
    []).

fof(rc2_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

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_arytm_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc3_arytm_3),
    []).

fof(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

fof(redefinition_k12_arytm_3,axiom,(
    k12_arytm_3 = k1_xboole_0 ),
    file(arytm_3,k12_arytm_3),
    []).

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

fof(t1_arytm_2,axiom,(
    r1_tarski(k6_arytm_3,k2_arytm_2) ),
    file(arytm_2,t1_arytm_2),
    []).

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_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t49_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( ! [C] : 
            ( m1_subset_1(C,A)
           => r2_hidden(C,B) )
       => A = B ) ) ),
    file(subset_1,t49_subset_1),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t64_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        & A != C ) ) ),
    file(zfmisc_1,t64_zfmisc_1),
    []).

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

fof(t71_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => r3_arytm_3(k12_arytm_3,A) ) ),
    file(arytm_3,t71_arytm_3),
    []).

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),
    []).