% Mizar ND problem: t4_altcat_1,altcat_1,84,20 
fof(dh_c1_6__altcat_1,definition,
    ( ! [A,B,C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ! [D] : 
            ( ( v1_relat_1(D)
              & v1_funct_1(D) )
           => ( ( r2_hidden(C,k1_funct_2(c1_6__altcat_1,A))
                & r2_hidden(D,k1_funct_2(A,B)) )
             => r2_hidden(k5_relat_1(C,D),k1_funct_2(c1_6__altcat_1,B)) ) ) )
   => ! [E,F,G,H] : 
        ( ( v1_relat_1(H)
          & v1_funct_1(H) )
       => ! [I] : 
            ( ( v1_relat_1(I)
              & v1_funct_1(I) )
           => ( ( r2_hidden(H,k1_funct_2(E,F))
                & r2_hidden(I,k1_funct_2(F,G)) )
             => r2_hidden(k5_relat_1(H,I),k1_funct_2(E,G)) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__altcat_1),file(altcat_1,c1_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c1_6__altcat_1)]).

fof(dh_c2_6__altcat_1,definition,
    ( ! [A,B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( r2_hidden(B,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
                & r2_hidden(C,k1_funct_2(c2_6__altcat_1,A)) )
             => r2_hidden(k5_relat_1(B,C),k1_funct_2(c1_6__altcat_1,A)) ) ) )
   => ! [D,E,F] : 
        ( ( v1_relat_1(F)
          & v1_funct_1(F) )
       => ! [G] : 
            ( ( v1_relat_1(G)
              & v1_funct_1(G) )
           => ( ( r2_hidden(F,k1_funct_2(c1_6__altcat_1,D))
                & r2_hidden(G,k1_funct_2(D,E)) )
             => r2_hidden(k5_relat_1(F,G),k1_funct_2(c1_6__altcat_1,E)) ) ) ) ),
    introduced(definition,[new_symbol(c2_6__altcat_1),file(altcat_1,c2_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c2_6__altcat_1)]).

fof(dh_c3_6__altcat_1,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( ( r2_hidden(A,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
                & r2_hidden(B,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
             => r2_hidden(k5_relat_1(A,B),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ) ) )
   => ! [C,D] : 
        ( ( v1_relat_1(D)
          & v1_funct_1(D) )
       => ! [E] : 
            ( ( v1_relat_1(E)
              & v1_funct_1(E) )
           => ( ( r2_hidden(D,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
                & r2_hidden(E,k1_funct_2(c2_6__altcat_1,C)) )
             => r2_hidden(k5_relat_1(D,E),k1_funct_2(c1_6__altcat_1,C)) ) ) ) ),
    introduced(definition,[new_symbol(c3_6__altcat_1),file(altcat_1,c3_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c3_6__altcat_1)]).

fof(dh_c4_6__altcat_1,definition,
    ( ( ( v1_relat_1(c4_6__altcat_1)
        & v1_funct_1(c4_6__altcat_1) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( ( r2_hidden(c4_6__altcat_1,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
              & r2_hidden(A,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
           => r2_hidden(k5_relat_1(c4_6__altcat_1,A),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( r2_hidden(B,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
                & r2_hidden(C,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
             => r2_hidden(k5_relat_1(B,C),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ) ) ) ),
    introduced(definition,[new_symbol(c4_6__altcat_1),file(altcat_1,c4_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c4_6__altcat_1)]).

fof(dh_c5_6__altcat_1,definition,
    ( ( ( v1_relat_1(c5_6__altcat_1)
        & v1_funct_1(c5_6__altcat_1) )
     => ( ( r2_hidden(c4_6__altcat_1,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
          & r2_hidden(c5_6__altcat_1,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
       => r2_hidden(k5_relat_1(c4_6__altcat_1,c5_6__altcat_1),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( ( r2_hidden(c4_6__altcat_1,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
            & r2_hidden(A,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
         => r2_hidden(k5_relat_1(c4_6__altcat_1,A),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ) ) ),
    introduced(definition,[new_symbol(c5_6__altcat_1),file(altcat_1,c5_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c5_6__altcat_1)]).

fof(e2_6__altcat_1,assumption,
    ( r2_hidden(c4_6__altcat_1,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
    & r2_hidden(c5_6__altcat_1,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) ),
    introduced(assumption,[file(altcat_1,e2_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,e2_6__altcat_1)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_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(cc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc1_tex_2)]).

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(rc2_tex_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc2_tex_2)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc3_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc3_tex_2)]).

fof(rc4_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc4_tex_2)]).

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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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(cc1_altcat_1,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_fraenkel(B) ) ) ),
    file(altcat_1,cc1_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,cc1_altcat_1)]).

fof(cc1_fraenkel,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc2_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc2_tex_2)]).

fof(fc10_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc10_relat_1)]).

fof(fc1_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,fc1_funct_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(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

fof(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]).

fof(fc9_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc9_relat_1)]).

fof(rc1_fraenkel,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

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_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_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(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(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(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(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

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_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    [interesting(0.9),axiom,file(funct_2,k1_funct_2)]).

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_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_1)]).

fof(dt_c1_6__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c1_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c1_6__altcat_1)]).

fof(dt_c3_6__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c3_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c3_6__altcat_1)]).

fof(dt_c4_6__altcat_1,assumption,
    ( v1_relat_1(c4_6__altcat_1)
    & v1_funct_1(c4_6__altcat_1) ),
    introduced(assumption,[file(altcat_1,c4_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c4_6__altcat_1)]).

fof(dt_c5_6__altcat_1,assumption,
    ( v1_relat_1(c5_6__altcat_1)
    & v1_funct_1(c5_6__altcat_1) ),
    introduced(assumption,[file(altcat_1,c5_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c5_6__altcat_1)]).

fof(fc1_fraenkel,theorem,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,fc1_fraenkel)]).

fof(fc1_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]).

fof(fc2_funct_2,theorem,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    [interesting(0.9),axiom,file(funct_2,fc2_funct_2)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_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(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(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(dt_c2_6__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c2_6__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c2_6__altcat_1)]).

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.9),axiom,file(funct_2,d2_funct_2)]).

fof(e3_6__altcat_1,plain,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & A = c4_6__altcat_1
        & k1_relat_1(A) = c1_6__altcat_1
        & r1_tarski(k2_relat_1(A),c2_6__altcat_1) )
    & ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & A = c5_6__altcat_1
        & k1_relat_1(A) = c2_6__altcat_1
        & r1_tarski(k2_relat_1(A),c3_6__altcat_1) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1,e2_6__altcat_1])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc1_tex_2,fc12_relat_1,fc4_relat_1,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_altcat_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_tex_2,fc1_funct_2,fc1_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_fraenkel,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_relat_1,dt_k2_relat_1,dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1,fc1_fraenkel,fc2_funct_2,rc1_funct_1,t1_subset,t3_subset,t7_boole,e2_6__altcat_1,d2_funct_2]),
    [interesting(0.8),file(altcat_1,e3_6__altcat_1),[file(altcat_1,e3_6__altcat_1)]]).

fof(t45_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)) ) ) ),
    file(relat_1,t45_relat_1),
    [interesting(0.9),axiom,file(relat_1,t45_relat_1)]).

fof(e1_6__altcat_1,plain,(
    r1_tarski(k2_relat_1(k5_relat_1(c4_6__altcat_1,c5_6__altcat_1)),k2_relat_1(c5_6__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_6__altcat_1,dt_c5_6__altcat_1])],[rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_tex_2,fc12_relat_1,fc4_relat_1,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_subset,t4_subset,t5_subset,t8_boole,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_tex_2,fc10_relat_1,fc6_relat_1,fc8_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_funct_1,fc1_subset_1,rc1_funct_1,reflexivity_r1_tarski,dt_k2_relat_1,dt_k5_relat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1,t3_subset,t45_relat_1]),
    [interesting(0.8),file(altcat_1,e1_6__altcat_1),[file(altcat_1,e1_6__altcat_1)]]).

fof(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.9),axiom,file(relat_1,t46_relat_1)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t1_xboole_1)]).

fof(e4_6__altcat_1,plain,
    ( k1_relat_1(k5_relat_1(c4_6__altcat_1,c5_6__altcat_1)) = c1_6__altcat_1
    & r1_tarski(k2_relat_1(k5_relat_1(c4_6__altcat_1,c5_6__altcat_1)),c3_6__altcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1,e2_6__altcat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1])],[rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_tex_2,fc12_relat_1,fc4_relat_1,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,t1_subset,t4_subset,t5_subset,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_tex_2,fc10_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k2_relat_1,dt_k5_relat_1,dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1,fc1_funct_1,rc1_funct_1,t3_subset,e3_6__altcat_1,e1_6__altcat_1,t46_relat_1,t1_xboole_1]),
    [interesting(0.8),file(altcat_1,e4_6__altcat_1),[file(altcat_1,e4_6__altcat_1)]]).

fof(e5_6__altcat_1,plain,(
    r2_hidden(k5_relat_1(c4_6__altcat_1,c5_6__altcat_1),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1,e2_6__altcat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc1_tex_2,fc12_relat_1,fc4_relat_1,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_altcat_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_tex_2,fc10_relat_1,fc1_funct_2,fc1_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_fraenkel,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_2,dt_k1_relat_1,dt_k2_relat_1,dt_k5_relat_1,dt_c1_6__altcat_1,dt_c3_6__altcat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1,fc1_fraenkel,fc1_funct_1,fc2_funct_2,rc1_funct_1,t1_subset,t3_subset,t7_boole,e4_6__altcat_1,d2_funct_2]),
    [interesting(0.8),file(altcat_1,e5_6__altcat_1),[file(altcat_1,e5_6__altcat_1)]]).

fof(i4_6__altcat_1,theorem,(
    $true ),
    introduced(tautology,[file(altcat_1,i4_6__altcat_1)]),
    [interesting(0.8),trivial,file(altcat_1,i4_6__altcat_1)]).

fof(i3_6__altcat_1,plain,(
    r2_hidden(k5_relat_1(c4_6__altcat_1,c5_6__altcat_1),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1,e2_6__altcat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1])],[e5_6__altcat_1,i4_6__altcat_1]),
    [interesting(0.8),file(altcat_1,i3_6__altcat_1),[file(altcat_1,i3_6__altcat_1)]]).

fof(i2_6__altcat_1,plain,
    ( ( r2_hidden(c4_6__altcat_1,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
      & r2_hidden(c5_6__altcat_1,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
   => r2_hidden(k5_relat_1(c4_6__altcat_1,c5_6__altcat_1),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1,dt_c4_6__altcat_1,dt_c5_6__altcat_1]),discharge_asm(discharge,[e2_6__altcat_1])],[e2_6__altcat_1,i3_6__altcat_1]),
    [interesting(0.8),file(altcat_1,i2_6__altcat_1),[file(altcat_1,i2_6__altcat_1)]]).

fof(i2_6_tmp__altcat_1,plain,
    ( ( v1_relat_1(c4_6__altcat_1)
      & v1_funct_1(c4_6__altcat_1)
      & v1_relat_1(c5_6__altcat_1)
      & v1_funct_1(c5_6__altcat_1) )
   => ( ( r2_hidden(c4_6__altcat_1,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
        & r2_hidden(c5_6__altcat_1,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
     => r2_hidden(k5_relat_1(c4_6__altcat_1,c5_6__altcat_1),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1]),discharge_asm(discharge,[dt_c4_6__altcat_1,dt_c5_6__altcat_1])],[dt_c4_6__altcat_1,dt_c5_6__altcat_1,i2_6__altcat_1]),
    [interesting(0.8),i1_6__altcat_1]).

fof(i1_6__altcat_1,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( r2_hidden(A,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
              & r2_hidden(B,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
           => r2_hidden(k5_relat_1(A,B),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1])],[i2_6_tmp__altcat_1,dh_c4_6__altcat_1,dh_c5_6__altcat_1]),
    [interesting(0.8),file(altcat_1,i1_6__altcat_1),[file(altcat_1,i1_6__altcat_1)]]).

fof(i1_6_tmp__altcat_1,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( r2_hidden(A,k1_funct_2(c1_6__altcat_1,c2_6__altcat_1))
              & r2_hidden(B,k1_funct_2(c2_6__altcat_1,c3_6__altcat_1)) )
           => r2_hidden(k5_relat_1(A,B),k1_funct_2(c1_6__altcat_1,c3_6__altcat_1)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1])],[dt_c1_6__altcat_1,dt_c2_6__altcat_1,dt_c3_6__altcat_1,i1_6__altcat_1]),
    [interesting(1),t4_altcat_1]).

fof(t4_altcat_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( ( r2_hidden(D,k1_funct_2(A,B))
              & r2_hidden(E,k1_funct_2(B,C)) )
           => r2_hidden(k5_relat_1(D,E),k1_funct_2(A,C)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__altcat_1,dh_c1_6__altcat_1,dh_c2_6__altcat_1,dh_c3_6__altcat_1]),
    [interesting(1),file(altcat_1,t4_altcat_1),[file(altcat_1,t4_altcat_1)]]).