% Mizar ND problem: t9_analoaf,analoaf,52,31 
fof(dh_c1_3__analoaf,definition,
    ( ( ( ~ v3_struct_0(c1_3__analoaf)
        & v3_rlvect_1(c1_3__analoaf)
        & v4_rlvect_1(c1_3__analoaf)
        & v5_rlvect_1(c1_3__analoaf)
        & v6_rlvect_1(c1_3__analoaf)
        & v7_rlvect_1(c1_3__analoaf)
        & l2_rlvect_1(c1_3__analoaf) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_3__analoaf))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(c1_3__analoaf))
                     => ( k4_rlvect_1(c1_3__analoaf,A,B) = k4_rlvect_1(c1_3__analoaf,C,D)
                       => k6_rlvect_1(c1_3__analoaf,A,D) = k6_rlvect_1(c1_3__analoaf,C,B) ) ) ) ) ) )
   => ! [E] : 
        ( ( ~ v3_struct_0(E)
          & v3_rlvect_1(E)
          & v4_rlvect_1(E)
          & v5_rlvect_1(E)
          & v6_rlvect_1(E)
          & v7_rlvect_1(E)
          & l2_rlvect_1(E) )
       => ! [F] : 
            ( m1_subset_1(F,u1_struct_0(E))
           => ! [G] : 
                ( m1_subset_1(G,u1_struct_0(E))
               => ! [H] : 
                    ( m1_subset_1(H,u1_struct_0(E))
                   => ! [I] : 
                        ( m1_subset_1(I,u1_struct_0(E))
                       => ( k4_rlvect_1(E,F,G) = k4_rlvect_1(E,H,I)
                         => k6_rlvect_1(E,F,I) = k6_rlvect_1(E,H,G) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__analoaf),file(analoaf,c1_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c1_3__analoaf)]).

fof(dh_c2_3__analoaf,definition,
    ( ( m1_subset_1(c2_3__analoaf,u1_struct_0(c1_3__analoaf))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_3__analoaf))
                 => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,A) = k4_rlvect_1(c1_3__analoaf,B,C)
                   => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,C) = k6_rlvect_1(c1_3__analoaf,B,A) ) ) ) ) )
   => ! [D] : 
        ( m1_subset_1(D,u1_struct_0(c1_3__analoaf))
       => ! [E] : 
            ( m1_subset_1(E,u1_struct_0(c1_3__analoaf))
           => ! [F] : 
                ( m1_subset_1(F,u1_struct_0(c1_3__analoaf))
               => ! [G] : 
                    ( m1_subset_1(G,u1_struct_0(c1_3__analoaf))
                   => ( k4_rlvect_1(c1_3__analoaf,D,E) = k4_rlvect_1(c1_3__analoaf,F,G)
                     => k6_rlvect_1(c1_3__analoaf,D,G) = k6_rlvect_1(c1_3__analoaf,F,E) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__analoaf),file(analoaf,c2_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c2_3__analoaf)]).

fof(dh_c3_3__analoaf,definition,
    ( ( m1_subset_1(c3_3__analoaf,u1_struct_0(c1_3__analoaf))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
             => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,A,B)
               => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,B) = k6_rlvect_1(c1_3__analoaf,A,c3_3__analoaf) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,u1_struct_0(c1_3__analoaf))
       => ! [D] : 
            ( m1_subset_1(D,u1_struct_0(c1_3__analoaf))
           => ! [E] : 
                ( m1_subset_1(E,u1_struct_0(c1_3__analoaf))
               => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,C) = k4_rlvect_1(c1_3__analoaf,D,E)
                 => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,E) = k6_rlvect_1(c1_3__analoaf,D,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_3__analoaf),file(analoaf,c3_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c3_3__analoaf)]).

fof(dh_c4_3__analoaf,definition,
    ( ( m1_subset_1(c4_3__analoaf,u1_struct_0(c1_3__analoaf))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
         => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,A)
           => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,A) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(c1_3__analoaf))
           => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,B,C)
             => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,C) = k6_rlvect_1(c1_3__analoaf,B,c3_3__analoaf) ) ) ) ),
    introduced(definition,[new_symbol(c4_3__analoaf),file(analoaf,c4_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c4_3__analoaf)]).

fof(dh_c5_3__analoaf,definition,
    ( ( m1_subset_1(c5_3__analoaf,u1_struct_0(c1_3__analoaf))
     => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,c5_3__analoaf)
       => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,c5_3__analoaf) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
       => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,A)
         => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,A) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ) ) ),
    introduced(definition,[new_symbol(c5_3__analoaf),file(analoaf,c5_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c5_3__analoaf)]).

fof(e1_3__analoaf,assumption,(
    k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,c5_3__analoaf) ),
    introduced(assumption,[file(analoaf,e1_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,e1_3__analoaf)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

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

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

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(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(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

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(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

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(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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(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(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

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(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(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(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(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_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(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_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

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_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(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

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(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(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(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_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(existence_l2_rlvect_1,axiom,(
    ? [A] : l2_rlvect_1(A) ),
    file(rlvect_1,l2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_1)]).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    [interesting(0.9),axiom,file(struct_0,l2_struct_0)]).

fof(redefinition_k1_domain_1,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    [interesting(0.9),axiom,file(domain_1,k1_domain_1)]).

fof(redefinition_k8_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    [interesting(0.9),axiom,file(domain_1,k1_domain_1)]).

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

fof(dt_k5_rlvect_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ),
    file(rlvect_1,k5_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k5_rlvect_1)]).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_l2_rlvect_1,axiom,(
    ! [A] : 
      ( l2_rlvect_1(A)
     => l1_rlvect_1(A) ) ),
    file(rlvect_1,l2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l2_rlvect_1)]).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    [interesting(0.9),axiom,file(struct_0,l2_struct_0)]).

fof(dt_u1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_funct_1(u1_rlvect_1(A))
        & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,u1_rlvect_1)]).

fof(dt_u2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ),
    file(struct_0,u2_struct_0),
    [interesting(0.9),axiom,file(struct_0,u2_struct_0)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(rc4_struct_0,theorem,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc4_struct_0)]).

fof(commutativity_k4_rlvect_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ),
    file(rlvect_1,k4_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]).

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(redefinition_k4_rlvect_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ),
    file(rlvect_1,k4_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]).

fof(dt_k1_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ),
    file(rlvect_1,k1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k1_rlvect_1)]).

fof(dt_k2_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k2_rlvect_1)]).

fof(dt_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k4_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]).

fof(dt_k6_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k6_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,k6_rlvect_1)]).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_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_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_3__analoaf,assumption,
    ( ~ v3_struct_0(c1_3__analoaf)
    & v3_rlvect_1(c1_3__analoaf)
    & v4_rlvect_1(c1_3__analoaf)
    & v5_rlvect_1(c1_3__analoaf)
    & v6_rlvect_1(c1_3__analoaf)
    & v7_rlvect_1(c1_3__analoaf)
    & l2_rlvect_1(c1_3__analoaf) ),
    introduced(assumption,[file(analoaf,c1_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c1_3__analoaf)]).

fof(dt_c2_3__analoaf,assumption,(
    m1_subset_1(c2_3__analoaf,u1_struct_0(c1_3__analoaf)) ),
    introduced(assumption,[file(analoaf,c2_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c2_3__analoaf)]).

fof(dt_c5_3__analoaf,assumption,(
    m1_subset_1(c5_3__analoaf,u1_struct_0(c1_3__analoaf)) ),
    introduced(assumption,[file(analoaf,c5_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c5_3__analoaf)]).

fof(d2_rlvect_1,definition,(
    ! [A] : 
      ( l2_struct_0(A)
     => k1_rlvect_1(A) = u2_struct_0(A) ) ),
    file(rlvect_1,d2_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,d2_rlvect_1)]).

fof(d3_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ),
    file(rlvect_1,d3_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,d3_rlvect_1)]).

fof(d11_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k6_rlvect_1(A,B,C) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) ) ) ) ),
    file(rlvect_1,d11_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,d11_rlvect_1)]).

fof(t10_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ),
    file(rlvect_1,t10_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,t10_rlvect_1)]).

fof(e1_3_1__analoaf,plain,(
    k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,c5_3__analoaf) = k6_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,k1_rlvect_1(c1_3__analoaf)),c5_3__analoaf) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__analoaf,dt_c2_3__analoaf,dt_c5_3__analoaf])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,fc4_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_zfmisc_1,dt_k5_rlvect_1,dt_k8_funct_2,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_u1_rlvect_1,dt_u2_struct_0,fc1_struct_0,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_k6_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__analoaf,dt_c2_3__analoaf,dt_c5_3__analoaf,d2_rlvect_1,d3_rlvect_1,d11_rlvect_1,t10_rlvect_1]),
    [interesting(0.65),file(analoaf,e1_3_1__analoaf),[file(analoaf,e1_3_1__analoaf)]]).

fof(dt_c3_3__analoaf,assumption,(
    m1_subset_1(c3_3__analoaf,u1_struct_0(c1_3__analoaf)) ),
    introduced(assumption,[file(analoaf,c3_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c3_3__analoaf)]).

fof(t28_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_rlvect_1(A,B,B) = k1_rlvect_1(A) ) ) ),
    file(rlvect_1,t28_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,t28_rlvect_1)]).

fof(e2_3_1__analoaf,plain,(
    k6_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,k1_rlvect_1(c1_3__analoaf)),c5_3__analoaf) = k6_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,k6_rlvect_1(c1_3__analoaf,c3_3__analoaf,c3_3__analoaf)),c5_3__analoaf) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__analoaf,dt_c2_3__analoaf,dt_c3_3__analoaf,dt_c5_3__analoaf])],[reflexivity_r1_tarski,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k1_zfmisc_1,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_xreal_0,cc7_xreal_0,fc1_subset_1,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_u1_rlvect_1,cc15_membered,fc4_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,dt_k2_rlvect_1,dt_k5_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_u2_struct_0,fc1_struct_0,rc3_struct_0,rc4_struct_0,d3_rlvect_1,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k1_rlvect_1,dt_k4_rlvect_1,dt_k6_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__analoaf,dt_c2_3__analoaf,dt_c3_3__analoaf,dt_c5_3__analoaf,d2_rlvect_1,d11_rlvect_1,t28_rlvect_1]),
    [interesting(0.65),file(analoaf,e2_3_1__analoaf),[file(analoaf,e2_3_1__analoaf)]]).

fof(dt_c4_3__analoaf,assumption,(
    m1_subset_1(c4_3__analoaf,u1_struct_0(c1_3__analoaf)) ),
    introduced(assumption,[file(analoaf,c4_3__analoaf)]),
    [interesting(0.8),axiom,file(analoaf,c4_3__analoaf)]).

fof(d6_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ),
    file(rlvect_1,d6_rlvect_1),
    [interesting(0.9),axiom,file(rlvect_1,d6_rlvect_1)]).

fof(e3_3_1__analoaf,plain,(
    k6_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,k6_rlvect_1(c1_3__analoaf,c3_3__analoaf,c3_3__analoaf)),c5_3__analoaf) = k6_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,c5_3__analoaf),k5_rlvect_1(c1_3__analoaf,c3_3__analoaf)),c5_3__analoaf) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__analoaf,dt_c2_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf,e1_3__analoaf])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,fc4_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_u1_rlvect_1,fc1_struct_0,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_k5_rlvect_1,dt_k6_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__analoaf,dt_c2_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf,d3_rlvect_1,d11_rlvect_1,e1_3__analoaf,d6_rlvect_1]),
    [interesting(0.65),file(analoaf,e3_3_1__analoaf),[file(analoaf,e3_3_1__analoaf)]]).

fof(e4_3_1__analoaf,plain,(
    k6_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,c5_3__analoaf),k5_rlvect_1(c1_3__analoaf,c3_3__analoaf)),c5_3__analoaf) = k4_rlvect_1(c1_3__analoaf,k5_rlvect_1(c1_3__analoaf,c3_3__analoaf),k6_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,c5_3__analoaf),c5_3__analoaf)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,fc4_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_u1_rlvect_1,fc1_struct_0,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_k5_rlvect_1,dt_k6_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf,d3_rlvect_1,d11_rlvect_1,d6_rlvect_1]),
    [interesting(0.65),file(analoaf,e4_3_1__analoaf),[file(analoaf,e4_3_1__analoaf)]]).

fof(t78_rlsub_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( B = k2_rlvect_1(A,C,D)
                  <=> C = k6_rlvect_1(A,B,D) ) ) ) ) ) ),
    file(rlsub_2,t78_rlsub_2),
    [interesting(0.9),axiom,file(rlsub_2,t78_rlsub_2)]).

fof(e5_3_1__analoaf,plain,(
    k4_rlvect_1(c1_3__analoaf,k5_rlvect_1(c1_3__analoaf,c3_3__analoaf),k6_rlvect_1(c1_3__analoaf,k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,c5_3__analoaf),c5_3__analoaf)) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,fc4_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,redefinition_k1_domain_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_u1_rlvect_1,fc1_struct_0,rc3_struct_0,rc4_struct_0,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k4_rlvect_1,dt_k2_rlvect_1,dt_k4_rlvect_1,dt_k5_rlvect_1,dt_k6_rlvect_1,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf,d3_rlvect_1,d11_rlvect_1,t78_rlsub_2]),
    [interesting(0.65),file(analoaf,e5_3_1__analoaf),[file(analoaf,e5_3_1__analoaf)]]).

fof(e2_3__analoaf,plain,(
    k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,c5_3__analoaf) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_3__analoaf,e1_3__analoaf,dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf])],[e1_3_1__analoaf,e2_3_1__analoaf,e3_3_1__analoaf,e4_3_1__analoaf,e5_3_1__analoaf]),
    [interesting(0.8),file(analoaf,e2_3__analoaf),[file(analoaf,e2_3__analoaf)]]).

fof(i7_3__analoaf,theorem,(
    $true ),
    introduced(tautology,[file(analoaf,i7_3__analoaf)]),
    [interesting(0.8),trivial,file(analoaf,i7_3__analoaf)]).

fof(i6_3__analoaf,plain,(
    k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,c5_3__analoaf) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_3__analoaf,e1_3__analoaf,dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf])],[e2_3__analoaf,i7_3__analoaf]),
    [interesting(0.8),file(analoaf,i6_3__analoaf),[file(analoaf,i6_3__analoaf)]]).

fof(i5_3__analoaf,plain,
    ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,c5_3__analoaf)
   => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,c5_3__analoaf) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__analoaf,dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf,dt_c5_3__analoaf]),discharge_asm(discharge,[e1_3__analoaf])],[e1_3__analoaf,i6_3__analoaf]),
    [interesting(0.8),file(analoaf,i5_3__analoaf),[file(analoaf,i5_3__analoaf)]]).

fof(i5_3_tmp__analoaf,plain,
    ( m1_subset_1(c5_3__analoaf,u1_struct_0(c1_3__analoaf))
   => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,c5_3__analoaf)
     => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,c5_3__analoaf) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__analoaf,dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf]),discharge_asm(discharge,[dt_c5_3__analoaf])],[dt_c5_3__analoaf,i5_3__analoaf]),
    [interesting(0.8),i4_3__analoaf]).

fof(i4_3__analoaf,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
     => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,A)
       => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,A) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_3__analoaf,dt_c1_3__analoaf,dt_c3_3__analoaf,dt_c4_3__analoaf])],[i5_3_tmp__analoaf,dh_c5_3__analoaf]),
    [interesting(0.8),file(analoaf,i4_3__analoaf),[file(analoaf,i4_3__analoaf)]]).

fof(i4_3_tmp__analoaf,plain,
    ( m1_subset_1(c4_3__analoaf,u1_struct_0(c1_3__analoaf))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
       => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,c4_3__analoaf,A)
         => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,A) = k6_rlvect_1(c1_3__analoaf,c4_3__analoaf,c3_3__analoaf) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__analoaf,dt_c1_3__analoaf,dt_c3_3__analoaf]),discharge_asm(discharge,[dt_c4_3__analoaf])],[dt_c4_3__analoaf,i4_3__analoaf]),
    [interesting(0.8),i3_3__analoaf]).

fof(i3_3__analoaf,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
         => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,A,B)
           => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,B) = k6_rlvect_1(c1_3__analoaf,A,c3_3__analoaf) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_3__analoaf,dt_c1_3__analoaf,dt_c3_3__analoaf])],[i4_3_tmp__analoaf,dh_c4_3__analoaf]),
    [interesting(0.8),file(analoaf,i3_3__analoaf),[file(analoaf,i3_3__analoaf)]]).

fof(i3_3_tmp__analoaf,plain,
    ( m1_subset_1(c3_3__analoaf,u1_struct_0(c1_3__analoaf))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
           => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,c3_3__analoaf) = k4_rlvect_1(c1_3__analoaf,A,B)
             => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,B) = k6_rlvect_1(c1_3__analoaf,A,c3_3__analoaf) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__analoaf,dt_c1_3__analoaf]),discharge_asm(discharge,[dt_c3_3__analoaf])],[dt_c3_3__analoaf,i3_3__analoaf]),
    [interesting(0.8),i2_3__analoaf]).

fof(i2_3__analoaf,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_3__analoaf))
             => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,A) = k4_rlvect_1(c1_3__analoaf,B,C)
               => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,C) = k6_rlvect_1(c1_3__analoaf,B,A) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_3__analoaf,dt_c1_3__analoaf])],[i3_3_tmp__analoaf,dh_c3_3__analoaf]),
    [interesting(0.8),file(analoaf,i2_3__analoaf),[file(analoaf,i2_3__analoaf)]]).

fof(i2_3_tmp__analoaf,plain,
    ( m1_subset_1(c2_3__analoaf,u1_struct_0(c1_3__analoaf))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_3__analoaf))
               => ( k4_rlvect_1(c1_3__analoaf,c2_3__analoaf,A) = k4_rlvect_1(c1_3__analoaf,B,C)
                 => k6_rlvect_1(c1_3__analoaf,c2_3__analoaf,C) = k6_rlvect_1(c1_3__analoaf,B,A) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__analoaf]),discharge_asm(discharge,[dt_c2_3__analoaf])],[dt_c2_3__analoaf,i2_3__analoaf]),
    [interesting(0.8),i1_3__analoaf]).

fof(i1_3__analoaf,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_3__analoaf))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(c1_3__analoaf))
                 => ( k4_rlvect_1(c1_3__analoaf,A,B) = k4_rlvect_1(c1_3__analoaf,C,D)
                   => k6_rlvect_1(c1_3__analoaf,A,D) = k6_rlvect_1(c1_3__analoaf,C,B) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__analoaf])],[i2_3_tmp__analoaf,dh_c2_3__analoaf]),
    [interesting(0.8),file(analoaf,i1_3__analoaf),[file(analoaf,i1_3__analoaf)]]).

fof(i1_3_tmp__analoaf,plain,
    ( ( ~ v3_struct_0(c1_3__analoaf)
      & v3_rlvect_1(c1_3__analoaf)
      & v4_rlvect_1(c1_3__analoaf)
      & v5_rlvect_1(c1_3__analoaf)
      & v6_rlvect_1(c1_3__analoaf)
      & v7_rlvect_1(c1_3__analoaf)
      & l2_rlvect_1(c1_3__analoaf) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_3__analoaf))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_3__analoaf))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_3__analoaf))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(c1_3__analoaf))
                   => ( k4_rlvect_1(c1_3__analoaf,A,B) = k4_rlvect_1(c1_3__analoaf,C,D)
                     => k6_rlvect_1(c1_3__analoaf,A,D) = k6_rlvect_1(c1_3__analoaf,C,B) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__analoaf])],[dt_c1_3__analoaf,i1_3__analoaf]),
    [interesting(1),t9_analoaf]).

fof(t9_analoaf,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k4_rlvect_1(A,B,C) = k4_rlvect_1(A,D,E)
                       => k6_rlvect_1(A,B,E) = k6_rlvect_1(A,D,C) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__analoaf,dh_c1_3__analoaf]),
    [interesting(1),file(analoaf,t9_analoaf),[file(analoaf,t9_analoaf)]]).