% Mizar ND problem: t1_bvfunc_2,bvfunc_2,58,35 
fof(dh_c1_3__bvfunc_2,definition,
    ( ( ~ v1_xboole_0(c1_3__bvfunc_2)
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_partit1(c1_3__bvfunc_2)))
         => ! [B] : 
              ( m1_subset_1(B,c1_3__bvfunc_2)
             => ? [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(c1_3__bvfunc_2))
                  & r2_hidden(B,C)
                  & ? [D] : 
                      ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & ? [E] : 
                          ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                          & k1_relat_1(D) = A
                          & k2_relat_1(D) = E
                          & ! [F] : 
                              ( r2_hidden(F,A)
                             => r2_hidden(k1_funct_1(D,F),F) )
                          & C = k8_setfam_1(c1_3__bvfunc_2,E)
                          & C != k1_xboole_0 ) ) ) ) ) )
   => ! [G] : 
        ( ~ v1_xboole_0(G)
       => ! [H] : 
            ( m1_subset_1(H,k1_zfmisc_1(k1_partit1(G)))
           => ! [I] : 
                ( m1_subset_1(I,G)
               => ? [J] : 
                    ( m1_subset_1(J,k1_zfmisc_1(G))
                    & r2_hidden(I,J)
                    & ? [K] : 
                        ( v1_relat_1(K)
                        & v1_funct_1(K)
                        & ? [L] : 
                            ( m1_subset_1(L,k1_zfmisc_1(k1_zfmisc_1(G)))
                            & k1_relat_1(K) = H
                            & k2_relat_1(K) = L
                            & ! [M] : 
                                ( r2_hidden(M,H)
                               => r2_hidden(k1_funct_1(K,M),M) )
                            & J = k8_setfam_1(G,L)
                            & J != k1_xboole_0 ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__bvfunc_2),file(bvfunc_2,c1_3__bvfunc_2)]),
    [interesting(0.8),axiom,file(bvfunc_2,c1_3__bvfunc_2)]).

fof(dh_c2_3__bvfunc_2,definition,
    ( ( m1_subset_1(c2_3__bvfunc_2,k1_zfmisc_1(k1_partit1(c1_3__bvfunc_2)))
     => ! [A] : 
          ( m1_subset_1(A,c1_3__bvfunc_2)
         => ? [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(c1_3__bvfunc_2))
              & r2_hidden(A,B)
              & ? [C] : 
                  ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & ? [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                      & k1_relat_1(C) = c2_3__bvfunc_2
                      & k2_relat_1(C) = D
                      & ! [E] : 
                          ( r2_hidden(E,c2_3__bvfunc_2)
                         => r2_hidden(k1_funct_1(C,E),E) )
                      & B = k8_setfam_1(c1_3__bvfunc_2,D)
                      & B != k1_xboole_0 ) ) ) ) )
   => ! [F] : 
        ( m1_subset_1(F,k1_zfmisc_1(k1_partit1(c1_3__bvfunc_2)))
       => ! [G] : 
            ( m1_subset_1(G,c1_3__bvfunc_2)
           => ? [H] : 
                ( m1_subset_1(H,k1_zfmisc_1(c1_3__bvfunc_2))
                & r2_hidden(G,H)
                & ? [I] : 
                    ( v1_relat_1(I)
                    & v1_funct_1(I)
                    & ? [J] : 
                        ( m1_subset_1(J,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                        & k1_relat_1(I) = F
                        & k2_relat_1(I) = J
                        & ! [K] : 
                            ( r2_hidden(K,F)
                           => r2_hidden(k1_funct_1(I,K),K) )
                        & H = k8_setfam_1(c1_3__bvfunc_2,J)
                        & H != k1_xboole_0 ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__bvfunc_2),file(bvfunc_2,c2_3__bvfunc_2)]),
    [interesting(0.8),axiom,file(bvfunc_2,c2_3__bvfunc_2)]).

fof(dh_c3_3__bvfunc_2,definition,
    ( ( m1_subset_1(c3_3__bvfunc_2,c1_3__bvfunc_2)
     => ? [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
          & r2_hidden(c3_3__bvfunc_2,A)
          & ? [B] : 
              ( v1_relat_1(B)
              & v1_funct_1(B)
              & ? [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                  & k1_relat_1(B) = c2_3__bvfunc_2
                  & k2_relat_1(B) = C
                  & ! [D] : 
                      ( r2_hidden(D,c2_3__bvfunc_2)
                     => r2_hidden(k1_funct_1(B,D),D) )
                  & A = k8_setfam_1(c1_3__bvfunc_2,C)
                  & A != k1_xboole_0 ) ) ) )
   => ! [E] : 
        ( m1_subset_1(E,c1_3__bvfunc_2)
       => ? [F] : 
            ( m1_subset_1(F,k1_zfmisc_1(c1_3__bvfunc_2))
            & r2_hidden(E,F)
            & ? [G] : 
                ( v1_relat_1(G)
                & v1_funct_1(G)
                & ? [H] : 
                    ( m1_subset_1(H,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                    & k1_relat_1(G) = c2_3__bvfunc_2
                    & k2_relat_1(G) = H
                    & ! [I] : 
                        ( r2_hidden(I,c2_3__bvfunc_2)
                       => r2_hidden(k1_funct_1(G,I),I) )
                    & F = k8_setfam_1(c1_3__bvfunc_2,H)
                    & F != k1_xboole_0 ) ) ) ) ),
    introduced(definition,[new_symbol(c3_3__bvfunc_2),file(bvfunc_2,c3_3__bvfunc_2)]),
    [interesting(0.8),axiom,file(bvfunc_2,c3_3__bvfunc_2)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(cc1_relset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_partit1,axiom,(
    $true ),
    file(partit1,k1_partit1),
    [interesting(0.9),axiom,file(partit1,k1_partit1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_m1_t_1topsp,axiom,(
    $true ),
    file(t_1topsp,m1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]).

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),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(fc1_partit1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_partit1(A)) ),
    file(partit1,fc1_partit1),
    [interesting(0.9),axiom,file(partit1,fc1_partit1)]).

fof(rc1_margrel1,theorem,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc1_t_1topsp,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_t_1topsp(B,A)
      & v1_t_1topsp(B,A) ) ),
    file(t_1topsp,rc1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,rc1_t_1topsp)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(rc3_t_1topsp,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_t_1topsp(B,A)
      & ~ v1_xboole_0(B)
      & v1_t_1topsp(B,A) ) ),
    file(t_1topsp,rc3_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,rc3_t_1topsp)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(redefinition_k1_bvfunc_2,definition,(
    ! [A] : k1_bvfunc_2(A) = k1_partit1(A) ),
    file(bvfunc_2,k1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k1_bvfunc_2)]).

fof(redefinition_k5_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    [interesting(0.9),axiom,file(relset_1,k5_relset_1)]).

fof(dt_k1_bvfunc_2,axiom,(
    ! [A] : 
      ( v1_t_1topsp(k1_bvfunc_2(A),A)
      & m1_t_1topsp(k1_bvfunc_2(A),A) ) ),
    file(bvfunc_2,k1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k1_bvfunc_2)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    [interesting(0.9),axiom,file(relset_1,k5_relset_1)]).

fof(dt_k8_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k8_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k8_setfam_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_c1_3__bvfunc_2,assumption,(
    ~ v1_xboole_0(c1_3__bvfunc_2) ),
    introduced(assumption,[file(bvfunc_2,c1_3__bvfunc_2)]),
    [interesting(0.8),axiom,file(bvfunc_2,c1_3__bvfunc_2)]).

fof(dt_c2_3__bvfunc_2,assumption,(
    m1_subset_1(c2_3__bvfunc_2,k1_zfmisc_1(k1_partit1(c1_3__bvfunc_2))) ),
    introduced(assumption,[file(bvfunc_2,c2_3__bvfunc_2)]),
    [interesting(0.8),axiom,file(bvfunc_2,c2_3__bvfunc_2)]).

fof(dt_c3_3__bvfunc_2,assumption,(
    m1_subset_1(c3_3__bvfunc_2,c1_3__bvfunc_2) ),
    introduced(assumption,[file(bvfunc_2,c3_3__bvfunc_2)]),
    [interesting(0.8),axiom,file(bvfunc_2,c3_3__bvfunc_2)]).

fof(dh_c4_3__bvfunc_2,definition,
    ( ? [A] : 
        ( v1_funct_1(A)
        & m2_relset_1(A,k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2))
        & ! [B] : 
            ( m1_bvfunc_2(B,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
           => ( r2_hidden(B,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),A))
            <=> r2_hidden(B,c2_3__bvfunc_2) ) )
        & ! [B] : 
            ( m1_bvfunc_2(B,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
           => ( r2_hidden(B,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),A))
             => k4_finseq_4(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),A,B) = k22_bvfunc_1(c1_3__bvfunc_2,c3_3__bvfunc_2,B) ) ) )
   => ( v1_funct_1(c4_3__bvfunc_2)
      & m2_relset_1(c4_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2))
      & ! [C] : 
          ( m1_bvfunc_2(C,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
         => ( r2_hidden(C,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
          <=> r2_hidden(C,c2_3__bvfunc_2) ) )
      & ! [C] : 
          ( m1_bvfunc_2(C,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
         => ( r2_hidden(C,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
           => k4_finseq_4(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2,C) = k22_bvfunc_1(c1_3__bvfunc_2,c3_3__bvfunc_2,C) ) ) ) ),
    introduced(definition,[new_symbol(c4_3__bvfunc_2),file(bvfunc_2,c4_3__bvfunc_2)]),
    [interesting(0.8),axiom,file(bvfunc_2,c4_3__bvfunc_2)]).

fof(rc2_t_1topsp,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_eqrel_1(B,A)
          & ~ v1_xboole_0(B)
          & v1_setfam_1(B) ) ) ),
    file(t_1topsp,rc2_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,rc2_t_1topsp)]).

fof(redefinition_m1_bvfunc_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ! [C] : 
          ( m1_bvfunc_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,m1_bvfunc_1)]).

fof(dt_k1_t_1topsp,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_subset_1(k1_t_1topsp(A,B,C),k1_zfmisc_1(A)) ) ),
    file(t_1topsp,k1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,k1_t_1topsp)]).

fof(dt_m1_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ! [C] : 
          ( m1_bvfunc_1(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(A)) ) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,m1_bvfunc_1)]).

fof(dt_m1_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,m1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,m1_eqrel_1)]).

fof(cc1_eqrel_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(eqrel_1,cc1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,cc1_eqrel_1)]).

fof(cc2_eqrel_1,theorem,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => v1_setfam_1(B) ) ),
    file(eqrel_1,cc2_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,cc2_eqrel_1)]).

fof(redefinition_k22_bvfunc_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => k22_bvfunc_1(A,B,C) = k1_t_1topsp(A,B,C) ) ),
    file(bvfunc_1,k22_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k22_bvfunc_1)]).

fof(redefinition_k4_relset_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(redefinition_m1_bvfunc_2,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_t_1topsp(B,A)
        & m1_t_1topsp(B,A) )
     => ! [C] : 
          ( m1_bvfunc_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(bvfunc_2,m1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,m1_bvfunc_2)]).

fof(dt_k22_bvfunc_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_bvfunc_1(k22_bvfunc_1(A,B,C),A,C) ) ),
    file(bvfunc_1,k22_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k22_bvfunc_1)]).

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,k4_finseq_4)]).

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),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(dt_m1_bvfunc_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_t_1topsp(B,A)
        & m1_t_1topsp(B,A) )
     => ! [C] : 
          ( m1_bvfunc_2(C,A,B)
         => m1_eqrel_1(C,A) ) ) ),
    file(bvfunc_2,m1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,m1_bvfunc_2)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(s2_partfun2__e1_3__bvfunc_2,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
        & m1_subset_1(C,A) )
     => ? [D] : 
          ( v1_funct_1(D)
          & m2_relset_1(D,k1_bvfunc_2(A),k1_zfmisc_1(A))
          & ! [E] : 
              ( m1_subset_1(E,k1_bvfunc_2(A))
             => ( r2_hidden(E,k4_relset_1(k1_bvfunc_2(A),k1_zfmisc_1(A),D))
              <=> r2_hidden(E,B) ) )
          & ! [E] : 
              ( m1_subset_1(E,k1_bvfunc_2(A))
             => ( r2_hidden(E,k4_relset_1(k1_bvfunc_2(A),k1_zfmisc_1(A),D))
               => k4_finseq_4(k1_bvfunc_2(A),k1_zfmisc_1(A),D,E) = k22_bvfunc_1(A,C,E) ) ) ) ) ),
    file(bvfunc_2,s2_partfun2__e1_3__bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,s2_partfun2__e1_3__bvfunc_2)]).

fof(e1_3__bvfunc_2,plain,(
    ? [A] : 
      ( v1_funct_1(A)
      & m2_relset_1(A,k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2))
      & ! [B] : 
          ( m1_bvfunc_2(B,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
         => ( r2_hidden(B,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),A))
          <=> r2_hidden(B,c2_3__bvfunc_2) ) )
      & ! [B] : 
          ( m1_bvfunc_2(B,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
         => ( r2_hidden(B,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),A))
           => k4_finseq_4(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),A,B) = k22_bvfunc_1(c1_3__bvfunc_2,c3_3__bvfunc_2,B) ) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[rc2_t_1topsp,redefinition_m1_bvfunc_1,dt_k1_relat_1,dt_k1_t_1topsp,dt_k2_zfmisc_1,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_t_1topsp,cc1_eqrel_1,cc1_relset_1,cc2_eqrel_1,fc4_subset_1,rc1_t_1topsp,rc3_t_1topsp,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k22_bvfunc_1,redefinition_k4_relset_1,redefinition_m1_bvfunc_2,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_partit1,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k4_finseq_4,dt_k4_relset_1,dt_m1_bvfunc_2,dt_m1_subset_1,dt_m2_relset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,fc1_partit1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,s2_partfun2__e1_3__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,e1_3__bvfunc_2),[file(bvfunc_2,e1_3__bvfunc_2)]]).

fof(dt_c4_3__bvfunc_2,plain,
    ( v1_funct_1(c4_3__bvfunc_2)
    & m2_relset_1(c4_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2)) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[dh_c4_3__bvfunc_2,e1_3__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,c4_3__bvfunc_2),[file(bvfunc_2,c4_3__bvfunc_2)]]).

fof(fc1_margrel1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(e1_3_6_1__bvfunc_2,assumption,(
    k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) = k1_xboole_0 ),
    introduced(assumption,[file(bvfunc_2,e1_3_6_1__bvfunc_2)]),
    [interesting(0.5),axiom,file(bvfunc_2,e1_3_6_1__bvfunc_2)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(existence_m1_t_1topsp,axiom,(
    ! [A] : 
    ? [B] : m1_t_1topsp(B,A) ),
    file(t_1topsp,m1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(de_c5_3__bvfunc_2,definition,(
    c5_3__bvfunc_2 = k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) ),
    introduced(definition,[new_symbol(c5_3__bvfunc_2),file(bvfunc_2,c5_3__bvfunc_2)]),
    [interesting(0.8),axiom,file(bvfunc_2,c5_3__bvfunc_2)]).

fof(e10_3__bvfunc_2,plain,(
    m1_subset_1(k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2),k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[rc1_margrel1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k2_relat_1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_k5_relset_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t3_subset]),
    [interesting(0.8),file(bvfunc_2,e10_3__bvfunc_2),[file(bvfunc_2,e10_3__bvfunc_2)]]).

fof(dt_c5_3__bvfunc_2,plain,(
    m1_subset_1(c5_3__bvfunc_2,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[rc1_margrel1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k2_relat_1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_k5_relset_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t3_subset,de_c5_3__bvfunc_2,e10_3__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,c5_3__bvfunc_2),[file(bvfunc_2,c5_3__bvfunc_2)]]).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k1_setfam_1)]).

fof(redefinition_k6_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]).

fof(dt_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]).

fof(d10_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( B != k1_xboole_0
         => k8_setfam_1(A,B) = k6_setfam_1(A,B) )
        & ( B = k1_xboole_0
         => k8_setfam_1(A,B) = A ) ) ) ),
    file(setfam_1,d10_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,d10_setfam_1)]).

fof(e2_3_6_1__bvfunc_2,plain,(
    k8_setfam_1(c1_3__bvfunc_2,c5_3__bvfunc_2) = c1_3__bvfunc_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_6_1__bvfunc_2])],[antisymmetry_r2_hidden,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_setfam_1,dt_k2_relat_1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,redefinition_k6_setfam_1,dt_k1_bvfunc_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_relset_1,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c4_3__bvfunc_2,dt_c5_3__bvfunc_2,de_c5_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0,t3_subset,t6_boole,e1_3_6_1__bvfunc_2,d10_setfam_1]),
    [interesting(0.5),file(bvfunc_2,e2_3_6_1__bvfunc_2),[file(bvfunc_2,e2_3_6_1__bvfunc_2)]]).

fof(dt_c1_3_2__bvfunc_2,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc_2,c1_3_2__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_2__bvfunc_2)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c1_3_2__bvfunc_2,definition,
    ( ~ ( r2_hidden(c1_3_2__bvfunc_2,c2_3__bvfunc_2)
        & ~ r2_hidden(c1_3_2__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) )
   => ! [A] : 
        ~ ( r2_hidden(A,c2_3__bvfunc_2)
          & ~ r2_hidden(A,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ) ),
    introduced(definition,[new_symbol(c1_3_2__bvfunc_2),file(bvfunc_2,c1_3_2__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_2__bvfunc_2)]).

fof(e1_3_2__bvfunc_2,assumption,(
    r2_hidden(c1_3_2__bvfunc_2,c2_3__bvfunc_2) ),
    introduced(assumption,[file(bvfunc_2,e1_3_2__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,e1_3_2__bvfunc_2)]).

fof(existence_m1_eqrel_1,axiom,(
    ! [A] : 
    ? [B] : m1_eqrel_1(B,A) ),
    file(eqrel_1,m1_eqrel_1),
    [interesting(0.9),axiom,file(eqrel_1,m1_eqrel_1)]).

fof(existence_m1_bvfunc_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_t_1topsp(B,A)
        & m1_t_1topsp(B,A) )
     => ? [C] : m1_bvfunc_2(C,A,B) ) ),
    file(bvfunc_2,m1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,m1_bvfunc_2)]).

fof(e2_3__bvfunc_2,plain,(
    ! [A] : 
      ( m1_bvfunc_2(A,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
     => ( r2_hidden(A,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
      <=> r2_hidden(A,c2_3__bvfunc_2) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[dh_c4_3__bvfunc_2,e1_3__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,e2_3__bvfunc_2),[file(bvfunc_2,e2_3__bvfunc_2)]]).

fof(e2_3_2__bvfunc_2,plain,(
    r2_hidden(c1_3_2__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_2__bvfunc_2,e1_3_2__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,rc2_t_1topsp,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_relat_1,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_bvfunc_2,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,redefinition_m1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_k4_relset_1,dt_m1_bvfunc_2,dt_c1_3__bvfunc_2,dt_c1_3_2__bvfunc_2,dt_c2_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t1_subset,t7_boole,e1_3_2__bvfunc_2,e2_3__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,e2_3_2__bvfunc_2),[file(bvfunc_2,e2_3_2__bvfunc_2)]]).

fof(i3_3_2__bvfunc_2,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_2,i3_3_2__bvfunc_2)]),
    [interesting(0.65),trivial,file(bvfunc_2,i3_3_2__bvfunc_2)]).

fof(i2_3_2__bvfunc_2,plain,(
    r2_hidden(c1_3_2__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_2__bvfunc_2,e1_3_2__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[e2_3_2__bvfunc_2,i3_3_2__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i2_3_2__bvfunc_2),[file(bvfunc_2,i2_3_2__bvfunc_2)]]).

fof(i1_3_2__bvfunc_2,plain,(
    ~ ( r2_hidden(c1_3_2__bvfunc_2,c2_3__bvfunc_2)
      & ~ r2_hidden(c1_3_2__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_2__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[e1_3_2__bvfunc_2])],[e1_3_2__bvfunc_2,i2_3_2__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i1_3_2__bvfunc_2),[file(bvfunc_2,i1_3_2__bvfunc_2)]]).

fof(i1_3_2_tmp__bvfunc_2,plain,(
    ~ ( r2_hidden(c1_3_2__bvfunc_2,c2_3__bvfunc_2)
      & ~ r2_hidden(c1_3_2__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[dt_c1_3_2__bvfunc_2])],[dt_c1_3_2__bvfunc_2,i1_3_2__bvfunc_2]),
    [interesting(0.8),e5_3__bvfunc_2]).

fof(e5_3__bvfunc_2,plain,(
    r1_tarski(c2_3__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ),
    inference(let,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[i1_3_2_tmp__bvfunc_2,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_k4_relset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,d3_tarski,dh_c1_3_2__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,e5_3__bvfunc_2),[file(bvfunc_2,e5_3__bvfunc_2)]]).

fof(dt_c1_3_1__bvfunc_2,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc_2,c1_3_1__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_1__bvfunc_2)]).

fof(dh_c1_3_1__bvfunc_2,definition,
    ( ~ ( r2_hidden(c1_3_1__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
        & ~ r2_hidden(c1_3_1__bvfunc_2,c2_3__bvfunc_2) )
   => ! [A] : 
        ~ ( r2_hidden(A,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
          & ~ r2_hidden(A,c2_3__bvfunc_2) ) ),
    introduced(definition,[new_symbol(c1_3_1__bvfunc_2),file(bvfunc_2,c1_3_1__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_1__bvfunc_2)]).

fof(e1_3_1__bvfunc_2,assumption,(
    r2_hidden(c1_3_1__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ),
    introduced(assumption,[file(bvfunc_2,e1_3_1__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,e1_3_1__bvfunc_2)]).

fof(e2_3_1__bvfunc_2,plain,(
    r2_hidden(c1_3_1__bvfunc_2,c2_3__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1__bvfunc_2,e1_3_1__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,rc2_t_1topsp,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_relat_1,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_bvfunc_2,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,redefinition_m1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_k4_relset_1,dt_m1_bvfunc_2,dt_c1_3__bvfunc_2,dt_c1_3_1__bvfunc_2,dt_c2_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t1_subset,t7_boole,e1_3_1__bvfunc_2,e2_3__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,e2_3_1__bvfunc_2),[file(bvfunc_2,e2_3_1__bvfunc_2)]]).

fof(i3_3_1__bvfunc_2,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_2,i3_3_1__bvfunc_2)]),
    [interesting(0.65),trivial,file(bvfunc_2,i3_3_1__bvfunc_2)]).

fof(i2_3_1__bvfunc_2,plain,(
    r2_hidden(c1_3_1__bvfunc_2,c2_3__bvfunc_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_1__bvfunc_2,e1_3_1__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[e2_3_1__bvfunc_2,i3_3_1__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i2_3_1__bvfunc_2),[file(bvfunc_2,i2_3_1__bvfunc_2)]]).

fof(i1_3_1__bvfunc_2,plain,(
    ~ ( r2_hidden(c1_3_1__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
      & ~ r2_hidden(c1_3_1__bvfunc_2,c2_3__bvfunc_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_1__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[e1_3_1__bvfunc_2])],[e1_3_1__bvfunc_2,i2_3_1__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i1_3_1__bvfunc_2),[file(bvfunc_2,i1_3_1__bvfunc_2)]]).

fof(i1_3_1_tmp__bvfunc_2,plain,(
    ~ ( r2_hidden(c1_3_1__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
      & ~ r2_hidden(c1_3_1__bvfunc_2,c2_3__bvfunc_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[dt_c1_3_1__bvfunc_2])],[dt_c1_3_1__bvfunc_2,i1_3_1__bvfunc_2]),
    [interesting(0.8),e4_3__bvfunc_2]).

fof(e4_3__bvfunc_2,plain,(
    r1_tarski(k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2),c2_3__bvfunc_2) ),
    inference(let,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[i1_3_1_tmp__bvfunc_2,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_k4_relset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,d3_tarski,dh_c1_3_1__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,e4_3__bvfunc_2),[file(bvfunc_2,e4_3__bvfunc_2)]]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(e6_3__bvfunc_2,plain,(
    k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) = c2_3__bvfunc_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[rc1_margrel1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_k4_relset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t3_subset,e5_3__bvfunc_2,e4_3__bvfunc_2,d10_xboole_0]),
    [interesting(0.8),file(bvfunc_2,e6_3__bvfunc_2),[file(bvfunc_2,e6_3__bvfunc_2)]]).

fof(dh_c1_3_3__bvfunc_2,definition,
    ( ( r2_hidden(c1_3_3__bvfunc_2,c2_3__bvfunc_2)
     => r2_hidden(k1_funct_1(c4_3__bvfunc_2,c1_3_3__bvfunc_2),c1_3_3__bvfunc_2) )
   => ! [A] : 
        ( r2_hidden(A,c2_3__bvfunc_2)
       => r2_hidden(k1_funct_1(c4_3__bvfunc_2,A),A) ) ),
    introduced(definition,[new_symbol(c1_3_3__bvfunc_2),file(bvfunc_2,c1_3_3__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_3__bvfunc_2)]).

fof(e1_3_3__bvfunc_2,assumption,(
    r2_hidden(c1_3_3__bvfunc_2,c2_3__bvfunc_2) ),
    introduced(assumption,[file(bvfunc_2,e1_3_3__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,e1_3_3__bvfunc_2)]).

fof(existence_m1_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ? [C] : m1_bvfunc_1(C,A,B) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,m1_bvfunc_1)]).

fof(dt_c1_3_3__bvfunc_2,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc_2,c1_3_3__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_3__bvfunc_2)]).

fof(de_c2_3_3__bvfunc_2,definition,(
    c2_3_3__bvfunc_2 = c1_3_3__bvfunc_2 ),
    introduced(definition,[new_symbol(c2_3_3__bvfunc_2),file(bvfunc_2,c2_3_3__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c2_3_3__bvfunc_2)]).

fof(d3_partit1,definition,(
    ! [A,B] : 
      ( B = k1_partit1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m1_eqrel_1(C,A) ) ) ),
    file(partit1,d3_partit1),
    [interesting(0.9),axiom,file(partit1,d3_partit1)]).

fof(e2_3_3__bvfunc_2,plain,(
    m1_eqrel_1(c1_3_3__bvfunc_2,c1_3__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c1_3_3__bvfunc_2,dt_c2_3__bvfunc_2,e1_3_3__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_t_1topsp,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_eqrel_1,dt_k1_partit1,dt_m1_eqrel_1,dt_c1_3__bvfunc_2,dt_c1_3_3__bvfunc_2,dt_c2_3__bvfunc_2,cc2_eqrel_1,fc1_partit1,t1_subset,t7_boole,e1_3_3__bvfunc_2,d3_partit1]),
    [interesting(0.65),file(bvfunc_2,e2_3_3__bvfunc_2),[file(bvfunc_2,e2_3_3__bvfunc_2)]]).

fof(dt_c2_3_3__bvfunc_2,plain,(
    m1_eqrel_1(c2_3_3__bvfunc_2,c1_3__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c1_3_3__bvfunc_2,dt_c2_3__bvfunc_2,e1_3_3__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_t_1topsp,rc2_xboole_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m1_eqrel_1,dt_m1_eqrel_1,dt_c1_3__bvfunc_2,dt_c1_3_3__bvfunc_2,cc2_eqrel_1,de_c2_3_3__bvfunc_2,e2_3_3__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,c2_3_3__bvfunc_2),[file(bvfunc_2,c2_3_3__bvfunc_2)]]).

fof(d4_finseq_4,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( r2_hidden(D,k1_relat_1(C))
         => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ),
    file(finseq_4,d4_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,d4_finseq_4)]).

fof(e3_3_3__bvfunc_2,plain,(
    k4_finseq_4(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2,c2_3_3__bvfunc_2) = k1_funct_1(c4_3__bvfunc_2,c2_3_3__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_3__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_3__bvfunc_2])],[rc1_margrel1,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,rc2_t_1topsp,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k2_zfmisc_1,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,cc1_eqrel_1,cc1_relset_1,cc2_eqrel_1,fc1_partit1,fc4_subset_1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_finseq_4,dt_k4_relset_1,dt_m2_relset_1,dt_c1_3__bvfunc_2,dt_c1_3_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c2_3_3__bvfunc_2,dt_c4_3__bvfunc_2,de_c2_3_3__bvfunc_2,fc1_subset_1,t1_subset,t3_subset,t7_boole,e5_3__bvfunc_2,e1_3_3__bvfunc_2,d4_finseq_4]),
    [interesting(0.65),file(bvfunc_2,e3_3_3__bvfunc_2),[file(bvfunc_2,e3_3_3__bvfunc_2)]]).

fof(e3_3__bvfunc_2,plain,(
    ! [A] : 
      ( m1_bvfunc_2(A,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
     => ( r2_hidden(A,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
       => k4_finseq_4(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2,A) = k22_bvfunc_1(c1_3__bvfunc_2,c3_3__bvfunc_2,A) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[dh_c4_3__bvfunc_2,e1_3__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,e3_3__bvfunc_2),[file(bvfunc_2,e3_3__bvfunc_2)]]).

fof(e4_3_3__bvfunc_2,plain,(
    k1_funct_1(c4_3__bvfunc_2,c2_3_3__bvfunc_2) = k22_bvfunc_1(c1_3__bvfunc_2,c3_3__bvfunc_2,c2_3_3__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_3__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_3__bvfunc_2])],[rc1_margrel1,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,rc2_t_1topsp,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m1_bvfunc_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_relat_1,dt_k1_t_1topsp,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_bvfunc_2,redefinition_k1_bvfunc_2,redefinition_k22_bvfunc_1,redefinition_k4_relset_1,redefinition_m1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k4_finseq_4,dt_k4_relset_1,dt_m1_bvfunc_2,dt_c1_3__bvfunc_2,dt_c1_3_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c2_3_3__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,de_c2_3_3__bvfunc_2,fc1_subset_1,t1_subset,t3_subset,t7_boole,e3_3_3__bvfunc_2,e3_3__bvfunc_2,e5_3__bvfunc_2,e1_3_3__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,e4_3_3__bvfunc_2),[file(bvfunc_2,e4_3_3__bvfunc_2)]]).

fof(e5_3_3__bvfunc_2,plain,(
    r2_hidden(k1_funct_1(c4_3__bvfunc_2,c1_3_3__bvfunc_2),c1_3_3__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_3__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_3__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_t_1topsp,cc1_relset_1,fc1_margrel1,fc1_partit1,fc1_xboole_0,fc4_subset_1,rc1_t_1topsp,rc2_t_1topsp,rc3_t_1topsp,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k1_bvfunc_2,redefinition_m1_bvfunc_1,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_relset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k22_bvfunc_1,dt_k1_funct_1,dt_k22_bvfunc_1,dt_c1_3__bvfunc_2,dt_c1_3_3__bvfunc_2,dt_c2_3_3__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,de_c2_3_3__bvfunc_2,t1_subset,t7_boole,e4_3_3__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,e5_3_3__bvfunc_2),[file(bvfunc_2,e5_3_3__bvfunc_2)]]).

fof(i3_3_3__bvfunc_2,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_2,i3_3_3__bvfunc_2)]),
    [interesting(0.65),trivial,file(bvfunc_2,i3_3_3__bvfunc_2)]).

fof(i2_3_3__bvfunc_2,plain,(
    r2_hidden(k1_funct_1(c4_3__bvfunc_2,c1_3_3__bvfunc_2),c1_3_3__bvfunc_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_3__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_3__bvfunc_2])],[e5_3_3__bvfunc_2,i3_3_3__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i2_3_3__bvfunc_2),[file(bvfunc_2,i2_3_3__bvfunc_2)]]).

fof(i1_3_3__bvfunc_2,plain,
    ( r2_hidden(c1_3_3__bvfunc_2,c2_3__bvfunc_2)
   => r2_hidden(k1_funct_1(c4_3__bvfunc_2,c1_3_3__bvfunc_2),c1_3_3__bvfunc_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_3__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[e1_3_3__bvfunc_2])],[e1_3_3__bvfunc_2,i2_3_3__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i1_3_3__bvfunc_2),[file(bvfunc_2,i1_3_3__bvfunc_2)]]).

fof(i1_3_3_tmp__bvfunc_2,plain,
    ( r2_hidden(c1_3_3__bvfunc_2,c2_3__bvfunc_2)
   => r2_hidden(k1_funct_1(c4_3__bvfunc_2,c1_3_3__bvfunc_2),c1_3_3__bvfunc_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[dt_c1_3_3__bvfunc_2])],[dt_c1_3_3__bvfunc_2,i1_3_3__bvfunc_2]),
    [interesting(0.8),e7_3__bvfunc_2]).

fof(e7_3__bvfunc_2,plain,(
    ! [A] : 
      ( r2_hidden(A,c2_3__bvfunc_2)
     => r2_hidden(k1_funct_1(c4_3__bvfunc_2,A),A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[i1_3_3_tmp__bvfunc_2,dh_c1_3_3__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,e7_3__bvfunc_2),[file(bvfunc_2,e7_3__bvfunc_2)]]).

fof(e3_3_6_1__bvfunc_2,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
      & r2_hidden(c3_3__bvfunc_2,A)
      & ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & ? [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
              & k1_relat_1(B) = c2_3__bvfunc_2
              & k2_relat_1(B) = C
              & ! [D] : 
                  ( r2_hidden(D,c2_3__bvfunc_2)
                 => r2_hidden(k1_funct_1(B,D),D) )
              & A = k8_setfam_1(c1_3__bvfunc_2,C)
              & A != k1_xboole_0 ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_3_6_1__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_k5_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k5_relset_1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k4_relset_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,dt_c5_3__bvfunc_2,de_c5_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e2_3_6_1__bvfunc_2,e6_3__bvfunc_2,e7_3__bvfunc_2]),
    [interesting(0.5),file(bvfunc_2,e3_3_6_1__bvfunc_2),[file(bvfunc_2,e3_3_6_1__bvfunc_2)]]).

fof(i2_3_6_1__bvfunc_2,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_2,i2_3_6_1__bvfunc_2)]),
    [interesting(0.5),trivial,file(bvfunc_2,i2_3_6_1__bvfunc_2)]).

fof(i1_3_6_1__bvfunc_2,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
      & r2_hidden(c3_3__bvfunc_2,A)
      & ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & ? [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
              & k1_relat_1(B) = c2_3__bvfunc_2
              & k2_relat_1(B) = C
              & ! [D] : 
                  ( r2_hidden(D,c2_3__bvfunc_2)
                 => r2_hidden(k1_funct_1(B,D),D) )
              & A = k8_setfam_1(c1_3__bvfunc_2,C)
              & A != k1_xboole_0 ) ) ) ),
    inference(conclusion,[status(thm),assumptions([e1_3_6_1__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[e3_3_6_1__bvfunc_2,i2_3_6_1__bvfunc_2]),
    [interesting(0.5),file(bvfunc_2,i1_3_6_1__bvfunc_2),[file(bvfunc_2,i1_3_6_1__bvfunc_2)]]).

fof(i1_3_6_1_tmp__bvfunc_2,plain,
    ( k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) = k1_xboole_0
   => ? [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
        & r2_hidden(c3_3__bvfunc_2,A)
        & ? [B] : 
            ( v1_relat_1(B)
            & v1_funct_1(B)
            & ? [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                & k1_relat_1(B) = c2_3__bvfunc_2
                & k2_relat_1(B) = C
                & ! [D] : 
                    ( r2_hidden(D,c2_3__bvfunc_2)
                   => r2_hidden(k1_funct_1(B,D),D) )
                & A = k8_setfam_1(c1_3__bvfunc_2,C)
                & A != k1_xboole_0 ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[e1_3_6_1__bvfunc_2])],[e1_3_6_1__bvfunc_2,i1_3_6_1__bvfunc_2]),
    [interesting(0.65),i1_3_6__bvfunc_2]).

fof(i1_3_6__bvfunc_2,plain,(
    ~ ( k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) = k1_xboole_0
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
         => ~ ( r2_hidden(c3_3__bvfunc_2,A)
              & ? [B] : 
                  ( v1_relat_1(B)
                  & v1_funct_1(B)
                  & ? [C] : 
                      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                      & k1_relat_1(B) = c2_3__bvfunc_2
                      & k2_relat_1(B) = C
                      & ! [D] : 
                          ( r2_hidden(D,c2_3__bvfunc_2)
                         => r2_hidden(k1_funct_1(B,D),D) )
                      & A = k8_setfam_1(c1_3__bvfunc_2,C)
                      & A != k1_xboole_0 ) ) ) ) ) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[i1_3_6_1_tmp__bvfunc_2,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k5_relset_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0]),
    [interesting(0.65),file(bvfunc_2,i1_3_6__bvfunc_2),[file(bvfunc_2,i1_3_6__bvfunc_2)]]).

fof(e1_3_6_2__bvfunc_2,assumption,(
    k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) != k1_xboole_0 ),
    introduced(assumption,[file(bvfunc_2,e1_3_6_2__bvfunc_2)]),
    [interesting(0.5),axiom,file(bvfunc_2,e1_3_6_2__bvfunc_2)]).

fof(e3_3_6_2__bvfunc_2,plain,(
    k8_setfam_1(c1_3__bvfunc_2,c5_3__bvfunc_2) = k6_setfam_1(c1_3__bvfunc_2,k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_6_2__bvfunc_2])],[antisymmetry_r2_hidden,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_setfam_1,dt_k2_relat_1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,redefinition_k6_setfam_1,dt_k1_bvfunc_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_relset_1,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c4_3__bvfunc_2,dt_c5_3__bvfunc_2,de_c5_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0,t3_subset,t6_boole,e1_3_6_2__bvfunc_2,d10_setfam_1]),
    [interesting(0.5),file(bvfunc_2,e3_3_6_2__bvfunc_2),[file(bvfunc_2,e3_3_6_2__bvfunc_2)]]).

fof(dh_c1_3_5__bvfunc_2,definition,
    ( ( r2_hidden(c1_3_5__bvfunc_2,k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
     => r2_hidden(c3_3__bvfunc_2,c1_3_5__bvfunc_2) )
   => ! [A] : 
        ( r2_hidden(A,k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
       => r2_hidden(c3_3__bvfunc_2,A) ) ),
    introduced(definition,[new_symbol(c1_3_5__bvfunc_2),file(bvfunc_2,c1_3_5__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_5__bvfunc_2)]).

fof(e1_3_5__bvfunc_2,assumption,(
    r2_hidden(c1_3_5__bvfunc_2,k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ),
    introduced(assumption,[file(bvfunc_2,e1_3_5__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,e1_3_5__bvfunc_2)]).

fof(dt_c1_3_5__bvfunc_2,assumption,(
    $true ),
    introduced(assumption,[file(bvfunc_2,c1_3_5__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_5__bvfunc_2)]).

fof(dh_c2_3_5__bvfunc_2,definition,
    ( ? [A] : 
        ( r2_hidden(A,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
        & c1_3_5__bvfunc_2 = k1_funct_1(c4_3__bvfunc_2,A) )
   => ( r2_hidden(c2_3_5__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
      & c1_3_5__bvfunc_2 = k1_funct_1(c4_3__bvfunc_2,c2_3_5__bvfunc_2) ) ),
    introduced(definition,[new_symbol(c2_3_5__bvfunc_2),file(bvfunc_2,c2_3_5__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c2_3_5__bvfunc_2)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e2_3_5__bvfunc_2,plain,(
    ? [A] : 
      ( r2_hidden(A,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
      & c1_3_5__bvfunc_2 = k1_funct_1(c4_3__bvfunc_2,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_5__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_5__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,redefinition_k5_relset_1,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k4_relset_1,dt_k5_relset_1,dt_c1_3__bvfunc_2,dt_c1_3_5__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t1_subset,t7_boole,e1_3_5__bvfunc_2,d5_funct_1]),
    [interesting(0.65),file(bvfunc_2,e2_3_5__bvfunc_2),[file(bvfunc_2,e2_3_5__bvfunc_2)]]).

fof(dt_c2_3_5__bvfunc_2,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3_5__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_5__bvfunc_2])],[dh_c2_3_5__bvfunc_2,e2_3_5__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,c2_3_5__bvfunc_2),[file(bvfunc_2,c2_3_5__bvfunc_2)]]).

fof(dh_c1_3_4__bvfunc_2,definition,
    ( ( m1_bvfunc_2(c1_3_4__bvfunc_2,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
     => ( r2_hidden(c1_3_4__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
       => r2_hidden(c3_3__bvfunc_2,k1_funct_1(c4_3__bvfunc_2,c1_3_4__bvfunc_2)) ) )
   => ! [A] : 
        ( m1_bvfunc_2(A,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
       => ( r2_hidden(A,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
         => r2_hidden(c3_3__bvfunc_2,k1_funct_1(c4_3__bvfunc_2,A)) ) ) ),
    introduced(definition,[new_symbol(c1_3_4__bvfunc_2),file(bvfunc_2,c1_3_4__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_4__bvfunc_2)]).

fof(e1_3_4__bvfunc_2,assumption,(
    r2_hidden(c1_3_4__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2)) ),
    introduced(assumption,[file(bvfunc_2,e1_3_4__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,e1_3_4__bvfunc_2)]).

fof(dt_c1_3_4__bvfunc_2,assumption,(
    m1_bvfunc_2(c1_3_4__bvfunc_2,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2)) ),
    introduced(assumption,[file(bvfunc_2,c1_3_4__bvfunc_2)]),
    [interesting(0.65),axiom,file(bvfunc_2,c1_3_4__bvfunc_2)]).

fof(e2_3_4__bvfunc_2,plain,(
    k4_finseq_4(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2,c1_3_4__bvfunc_2) = k22_bvfunc_1(c1_3__bvfunc_2,c3_3__bvfunc_2,c1_3_4__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__bvfunc_2,e1_3_4__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,rc2_t_1topsp,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m1_bvfunc_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_relat_1,dt_k1_t_1topsp,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_bvfunc_2,redefinition_k1_bvfunc_2,redefinition_k22_bvfunc_1,redefinition_k4_relset_1,redefinition_m1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k4_finseq_4,dt_k4_relset_1,dt_m1_bvfunc_2,dt_c1_3__bvfunc_2,dt_c1_3_4__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t1_subset,t7_boole,e1_3_4__bvfunc_2,e3_3__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,e2_3_4__bvfunc_2),[file(bvfunc_2,e2_3_4__bvfunc_2)]]).

fof(e3_3_4__bvfunc_2,plain,(
    k1_funct_1(c4_3__bvfunc_2,c1_3_4__bvfunc_2) = k22_bvfunc_1(c1_3__bvfunc_2,c3_3__bvfunc_2,c1_3_4__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_4__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,dt_k1_xboole_0,fc1_margrel1,fc1_xboole_0,rc2_t_1topsp,existence_m1_bvfunc_1,existence_m1_bvfunc_2,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,redefinition_m1_bvfunc_1,redefinition_m1_bvfunc_2,dt_k1_partit1,dt_k1_t_1topsp,dt_k2_zfmisc_1,dt_m1_bvfunc_1,dt_m1_bvfunc_2,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,cc1_eqrel_1,cc1_relset_1,cc2_eqrel_1,fc1_partit1,fc4_subset_1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k1_bvfunc_2,redefinition_k22_bvfunc_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k4_finseq_4,dt_k4_relset_1,dt_m2_relset_1,dt_c1_3__bvfunc_2,dt_c1_3_4__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t1_subset,t7_boole,e2_3_4__bvfunc_2,e1_3_4__bvfunc_2,d4_finseq_4]),
    [interesting(0.65),file(bvfunc_2,e3_3_4__bvfunc_2),[file(bvfunc_2,e3_3_4__bvfunc_2)]]).

fof(d1_t_1topsp,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( D = k1_t_1topsp(A,B,C)
                  <=> ( r2_hidden(B,D)
                      & r2_hidden(D,C) ) ) ) ) ) ) ),
    file(t_1topsp,d1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,d1_t_1topsp)]).

fof(e4_3_4__bvfunc_2,plain,(
    r2_hidden(c3_3__bvfunc_2,k1_funct_1(c4_3__bvfunc_2,c1_3_4__bvfunc_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_4__bvfunc_2])],[existence_m1_relset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_t_1topsp,cc1_relset_1,fc1_partit1,fc4_subset_1,rc1_margrel1,rc1_t_1topsp,rc3_t_1topsp,reflexivity_r1_tarski,existence_m1_bvfunc_1,existence_m1_bvfunc_2,existence_m2_relset_1,redefinition_k1_bvfunc_2,redefinition_m1_bvfunc_1,redefinition_m1_bvfunc_2,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_xboole_0,dt_m1_bvfunc_1,dt_m1_bvfunc_2,dt_m2_relset_1,fc1_margrel1,fc1_xboole_0,rc2_t_1topsp,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_funct_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c1_3_4__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e3_3_4__bvfunc_2,d1_t_1topsp]),
    [interesting(0.65),file(bvfunc_2,e4_3_4__bvfunc_2),[file(bvfunc_2,e4_3_4__bvfunc_2)]]).

fof(i3_3_4__bvfunc_2,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_2,i3_3_4__bvfunc_2)]),
    [interesting(0.65),trivial,file(bvfunc_2,i3_3_4__bvfunc_2)]).

fof(i2_3_4__bvfunc_2,plain,(
    r2_hidden(c3_3__bvfunc_2,k1_funct_1(c4_3__bvfunc_2,c1_3_4__bvfunc_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_4__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_4__bvfunc_2])],[e4_3_4__bvfunc_2,i3_3_4__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i2_3_4__bvfunc_2),[file(bvfunc_2,i2_3_4__bvfunc_2)]]).

fof(i1_3_4__bvfunc_2,plain,
    ( r2_hidden(c1_3_4__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
   => r2_hidden(c3_3__bvfunc_2,k1_funct_1(c4_3__bvfunc_2,c1_3_4__bvfunc_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_4__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[e1_3_4__bvfunc_2])],[e1_3_4__bvfunc_2,i2_3_4__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i1_3_4__bvfunc_2),[file(bvfunc_2,i1_3_4__bvfunc_2)]]).

fof(i1_3_4_tmp__bvfunc_2,plain,
    ( m1_bvfunc_2(c1_3_4__bvfunc_2,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
   => ( r2_hidden(c1_3_4__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
     => r2_hidden(c3_3__bvfunc_2,k1_funct_1(c4_3__bvfunc_2,c1_3_4__bvfunc_2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[dt_c1_3_4__bvfunc_2])],[dt_c1_3_4__bvfunc_2,i1_3_4__bvfunc_2]),
    [interesting(0.8),e8_3__bvfunc_2]).

fof(e8_3__bvfunc_2,plain,(
    ! [A] : 
      ( m1_bvfunc_2(A,c1_3__bvfunc_2,k1_bvfunc_2(c1_3__bvfunc_2))
     => ( r2_hidden(A,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
       => r2_hidden(c3_3__bvfunc_2,k1_funct_1(c4_3__bvfunc_2,A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[i1_3_4_tmp__bvfunc_2,dh_c1_3_4__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,e8_3__bvfunc_2),[file(bvfunc_2,e8_3__bvfunc_2)]]).

fof(e3_3_5__bvfunc_2,plain,
    ( r2_hidden(c2_3_5__bvfunc_2,k4_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
    & c1_3_5__bvfunc_2 = k1_funct_1(c4_3__bvfunc_2,c2_3_5__bvfunc_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_3_5__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_5__bvfunc_2])],[dh_c2_3_5__bvfunc_2,e2_3_5__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,e3_3_5__bvfunc_2),[file(bvfunc_2,e3_3_5__bvfunc_2)]]).

fof(e4_3_5__bvfunc_2,plain,(
    r2_hidden(c3_3__bvfunc_2,c1_3_5__bvfunc_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_5__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_5__bvfunc_2])],[rc1_margrel1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,fc1_margrel1,fc1_xboole_0,fc4_subset_1,rc2_t_1topsp,existence_m1_eqrel_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_relat_1,dt_m1_eqrel_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_partit1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_bvfunc_2,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,redefinition_m1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k4_relset_1,dt_m1_bvfunc_2,dt_c1_3__bvfunc_2,dt_c1_3_5__bvfunc_2,dt_c2_3_5__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_subset_1,t1_subset,t7_boole,e8_3__bvfunc_2,e3_3_5__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,e4_3_5__bvfunc_2),[file(bvfunc_2,e4_3_5__bvfunc_2)]]).

fof(i3_3_5__bvfunc_2,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_2,i3_3_5__bvfunc_2)]),
    [interesting(0.65),trivial,file(bvfunc_2,i3_3_5__bvfunc_2)]).

fof(i2_3_5__bvfunc_2,plain,(
    r2_hidden(c3_3__bvfunc_2,c1_3_5__bvfunc_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_5__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,e1_3_5__bvfunc_2])],[e4_3_5__bvfunc_2,i3_3_5__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i2_3_5__bvfunc_2),[file(bvfunc_2,i2_3_5__bvfunc_2)]]).

fof(i1_3_5__bvfunc_2,plain,
    ( r2_hidden(c1_3_5__bvfunc_2,k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
   => r2_hidden(c3_3__bvfunc_2,c1_3_5__bvfunc_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_5__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[e1_3_5__bvfunc_2])],[e1_3_5__bvfunc_2,i2_3_5__bvfunc_2]),
    [interesting(0.65),file(bvfunc_2,i1_3_5__bvfunc_2),[file(bvfunc_2,i1_3_5__bvfunc_2)]]).

fof(i1_3_5_tmp__bvfunc_2,plain,
    ( r2_hidden(c1_3_5__bvfunc_2,k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
   => r2_hidden(c3_3__bvfunc_2,c1_3_5__bvfunc_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[dt_c1_3_5__bvfunc_2])],[dt_c1_3_5__bvfunc_2,i1_3_5__bvfunc_2]),
    [interesting(0.8),e9_3__bvfunc_2]).

fof(e9_3__bvfunc_2,plain,(
    ! [A] : 
      ( r2_hidden(A,k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))
     => r2_hidden(c3_3__bvfunc_2,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[i1_3_5_tmp__bvfunc_2,dh_c1_3_5__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,e9_3__bvfunc_2),[file(bvfunc_2,e9_3__bvfunc_2)]]).

fof(d1_setfam_1,definition,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,d1_setfam_1)]).

fof(e2_3_6_2__bvfunc_2,plain,(
    r2_hidden(c3_3__bvfunc_2,k6_setfam_1(c1_3__bvfunc_2,k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2))) ),
    inference(mizar_by,[status(thm),assumptions([e1_3_6_2__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k2_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,redefinition_k6_setfam_1,dt_k1_bvfunc_2,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_relset_1,dt_k6_setfam_1,dt_c1_3__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0,t1_subset,t6_boole,t7_boole,e1_3_6_2__bvfunc_2,e9_3__bvfunc_2,d1_setfam_1]),
    [interesting(0.5),file(bvfunc_2,e2_3_6_2__bvfunc_2),[file(bvfunc_2,e2_3_6_2__bvfunc_2)]]).

fof(e4_3_6_2__bvfunc_2,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
      & r2_hidden(c3_3__bvfunc_2,A)
      & ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & ? [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
              & k1_relat_1(B) = c2_3__bvfunc_2
              & k2_relat_1(B) = C
              & ! [D] : 
                  ( r2_hidden(D,c2_3__bvfunc_2)
                 => r2_hidden(k1_funct_1(B,D),D) )
              & A = k8_setfam_1(c1_3__bvfunc_2,C)
              & A != k1_xboole_0 ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_3_6_2__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k1_setfam_1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k1_bvfunc_2,redefinition_k4_relset_1,redefinition_k5_relset_1,redefinition_k6_setfam_1,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k4_relset_1,dt_k5_relset_1,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,dt_c5_3__bvfunc_2,de_c5_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e3_3_6_2__bvfunc_2,e6_3__bvfunc_2,e7_3__bvfunc_2,e2_3_6_2__bvfunc_2]),
    [interesting(0.5),file(bvfunc_2,e4_3_6_2__bvfunc_2),[file(bvfunc_2,e4_3_6_2__bvfunc_2)]]).

fof(i2_3_6_2__bvfunc_2,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_2,i2_3_6_2__bvfunc_2)]),
    [interesting(0.5),trivial,file(bvfunc_2,i2_3_6_2__bvfunc_2)]).

fof(i1_3_6_2__bvfunc_2,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
      & r2_hidden(c3_3__bvfunc_2,A)
      & ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & ? [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
              & k1_relat_1(B) = c2_3__bvfunc_2
              & k2_relat_1(B) = C
              & ! [D] : 
                  ( r2_hidden(D,c2_3__bvfunc_2)
                 => r2_hidden(k1_funct_1(B,D),D) )
              & A = k8_setfam_1(c1_3__bvfunc_2,C)
              & A != k1_xboole_0 ) ) ) ),
    inference(conclusion,[status(thm),assumptions([e1_3_6_2__bvfunc_2,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[e4_3_6_2__bvfunc_2,i2_3_6_2__bvfunc_2]),
    [interesting(0.5),file(bvfunc_2,i1_3_6_2__bvfunc_2),[file(bvfunc_2,i1_3_6_2__bvfunc_2)]]).

fof(i1_3_6_2_tmp__bvfunc_2,plain,
    ( k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) != k1_xboole_0
   => ? [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
        & r2_hidden(c3_3__bvfunc_2,A)
        & ? [B] : 
            ( v1_relat_1(B)
            & v1_funct_1(B)
            & ? [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                & k1_relat_1(B) = c2_3__bvfunc_2
                & k2_relat_1(B) = C
                & ! [D] : 
                    ( r2_hidden(D,c2_3__bvfunc_2)
                   => r2_hidden(k1_funct_1(B,D),D) )
                & A = k8_setfam_1(c1_3__bvfunc_2,C)
                & A != k1_xboole_0 ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2]),discharge_asm(discharge,[e1_3_6_2__bvfunc_2])],[e1_3_6_2__bvfunc_2,i1_3_6_2__bvfunc_2]),
    [interesting(0.65),i2_3_6__bvfunc_2]).

fof(i2_3_6__bvfunc_2,plain,(
    ~ ( k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) != k1_xboole_0
      & ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
         => ~ ( r2_hidden(c3_3__bvfunc_2,A)
              & ? [B] : 
                  ( v1_relat_1(B)
                  & v1_funct_1(B)
                  & ? [C] : 
                      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                      & k1_relat_1(B) = c2_3__bvfunc_2
                      & k2_relat_1(B) = C
                      & ! [D] : 
                          ( r2_hidden(D,c2_3__bvfunc_2)
                         => r2_hidden(k1_funct_1(B,D),D) )
                      & A = k8_setfam_1(c1_3__bvfunc_2,C)
                      & A != k1_xboole_0 ) ) ) ) ) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[i1_3_6_2_tmp__bvfunc_2,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k5_relset_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0]),
    [interesting(0.65),file(bvfunc_2,i2_3_6__bvfunc_2),[file(bvfunc_2,i2_3_6__bvfunc_2)]]).

fof(e1_3_6__bvfunc_2,plain,(
    ~ ( k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) != k1_xboole_0
      & k5_relset_1(k1_bvfunc_2(c1_3__bvfunc_2),k1_zfmisc_1(c1_3__bvfunc_2),c4_3__bvfunc_2) = k1_xboole_0 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_k2_relat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,t2_subset,t3_subset,t7_boole,t8_boole,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,dt_k1_bvfunc_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_relset_1,dt_c1_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0,t6_boole]),
    [interesting(0.65),file(bvfunc_2,e1_3_6__bvfunc_2),[file(bvfunc_2,e1_3_6__bvfunc_2)]]).

fof(i3_3__bvfunc_2,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
      & r2_hidden(c3_3__bvfunc_2,A)
      & ? [B] : 
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & ? [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
              & k1_relat_1(B) = c2_3__bvfunc_2
              & k2_relat_1(B) = C
              & ! [D] : 
                  ( r2_hidden(D,c2_3__bvfunc_2)
                 => r2_hidden(k1_funct_1(B,D),D) )
              & A = k8_setfam_1(c1_3__bvfunc_2,C)
              & A != k1_xboole_0 ) ) ) ),
    inference(percases,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2])],[dt_k2_zfmisc_1,cc1_relset_1,fc4_subset_1,redefinition_m2_relset_1,dt_k1_partit1,dt_m1_relset_1,dt_m1_t_1topsp,dt_m2_relset_1,fc1_partit1,rc1_margrel1,rc1_subset_1,rc1_t_1topsp,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_t_1topsp,antisymmetry_r2_hidden,redefinition_k1_bvfunc_2,redefinition_k5_relset_1,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k5_relset_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2,dt_c3_3__bvfunc_2,dt_c4_3__bvfunc_2,fc1_margrel1,fc1_subset_1,fc1_xboole_0,i1_3_6__bvfunc_2,i2_3_6__bvfunc_2,e1_3_6__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,i3_3__bvfunc_2),[file(bvfunc_2,i3_3__bvfunc_2)]]).

fof(i3_3_tmp__bvfunc_2,plain,
    ( m1_subset_1(c3_3__bvfunc_2,c1_3__bvfunc_2)
   => ? [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c1_3__bvfunc_2))
        & r2_hidden(c3_3__bvfunc_2,A)
        & ? [B] : 
            ( v1_relat_1(B)
            & v1_funct_1(B)
            & ? [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                & k1_relat_1(B) = c2_3__bvfunc_2
                & k2_relat_1(B) = C
                & ! [D] : 
                    ( r2_hidden(D,c2_3__bvfunc_2)
                   => r2_hidden(k1_funct_1(B,D),D) )
                & A = k8_setfam_1(c1_3__bvfunc_2,C)
                & A != k1_xboole_0 ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2]),discharge_asm(discharge,[dt_c3_3__bvfunc_2])],[dt_c3_3__bvfunc_2,i3_3__bvfunc_2]),
    [interesting(0.8),i2_3__bvfunc_2]).

fof(i2_3__bvfunc_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,c1_3__bvfunc_2)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(c1_3__bvfunc_2))
          & r2_hidden(A,B)
          & ? [C] : 
              ( v1_relat_1(C)
              & v1_funct_1(C)
              & ? [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                  & k1_relat_1(C) = c2_3__bvfunc_2
                  & k2_relat_1(C) = D
                  & ! [E] : 
                      ( r2_hidden(E,c2_3__bvfunc_2)
                     => r2_hidden(k1_funct_1(C,E),E) )
                  & B = k8_setfam_1(c1_3__bvfunc_2,D)
                  & B != k1_xboole_0 ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__bvfunc_2,dt_c2_3__bvfunc_2])],[i3_3_tmp__bvfunc_2,dh_c3_3__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,i2_3__bvfunc_2),[file(bvfunc_2,i2_3__bvfunc_2)]]).

fof(i2_3_tmp__bvfunc_2,plain,
    ( m1_subset_1(c2_3__bvfunc_2,k1_zfmisc_1(k1_partit1(c1_3__bvfunc_2)))
   => ! [A] : 
        ( m1_subset_1(A,c1_3__bvfunc_2)
       => ? [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(c1_3__bvfunc_2))
            & r2_hidden(A,B)
            & ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                    & k1_relat_1(C) = c2_3__bvfunc_2
                    & k2_relat_1(C) = D
                    & ! [E] : 
                        ( r2_hidden(E,c2_3__bvfunc_2)
                       => r2_hidden(k1_funct_1(C,E),E) )
                    & B = k8_setfam_1(c1_3__bvfunc_2,D)
                    & B != k1_xboole_0 ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__bvfunc_2]),discharge_asm(discharge,[dt_c2_3__bvfunc_2])],[dt_c2_3__bvfunc_2,i2_3__bvfunc_2]),
    [interesting(0.8),i1_3__bvfunc_2]).

fof(i1_3__bvfunc_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_partit1(c1_3__bvfunc_2)))
     => ! [B] : 
          ( m1_subset_1(B,c1_3__bvfunc_2)
         => ? [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(c1_3__bvfunc_2))
              & r2_hidden(B,C)
              & ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & ? [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                      & k1_relat_1(D) = A
                      & k2_relat_1(D) = E
                      & ! [F] : 
                          ( r2_hidden(F,A)
                         => r2_hidden(k1_funct_1(D,F),F) )
                      & C = k8_setfam_1(c1_3__bvfunc_2,E)
                      & C != k1_xboole_0 ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__bvfunc_2])],[i2_3_tmp__bvfunc_2,dh_c2_3__bvfunc_2]),
    [interesting(0.8),file(bvfunc_2,i1_3__bvfunc_2),[file(bvfunc_2,i1_3__bvfunc_2)]]).

fof(i1_3_tmp__bvfunc_2,plain,
    ( ~ v1_xboole_0(c1_3__bvfunc_2)
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_partit1(c1_3__bvfunc_2)))
       => ! [B] : 
            ( m1_subset_1(B,c1_3__bvfunc_2)
           => ? [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(c1_3__bvfunc_2))
                & r2_hidden(B,C)
                & ? [D] : 
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & ? [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(c1_3__bvfunc_2)))
                        & k1_relat_1(D) = A
                        & k2_relat_1(D) = E
                        & ! [F] : 
                            ( r2_hidden(F,A)
                           => r2_hidden(k1_funct_1(D,F),F) )
                        & C = k8_setfam_1(c1_3__bvfunc_2,E)
                        & C != k1_xboole_0 ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__bvfunc_2])],[dt_c1_3__bvfunc_2,i1_3__bvfunc_2]),
    [interesting(1),t1_bvfunc_2]).

fof(t1_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ? [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                  & r2_hidden(C,D)
                  & ? [E] : 
                      ( v1_relat_1(E)
                      & v1_funct_1(E)
                      & ? [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(A)))
                          & k1_relat_1(E) = B
                          & k2_relat_1(E) = F
                          & ! [G] : 
                              ( r2_hidden(G,B)
                             => r2_hidden(k1_funct_1(E,G),G) )
                          & D = k8_setfam_1(A,F)
                          & D != k1_xboole_0 ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__bvfunc_2,dh_c1_3__bvfunc_2]),
    [interesting(1),file(bvfunc_2,t1_bvfunc_2),[file(bvfunc_2,t1_bvfunc_2)]]).