% Mizar ND problem: t4_funct_3,funct_3,62,56 
fof(dh_c1_4__funct_3,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(A,B)))
                & v2_funct_1(B) )
             => r1_tarski(k10_relat_1(B,c1_4__funct_3),k2_relat_1(A)) ) ) )
   => ! [C,D] : 
        ( ( v1_relat_1(D)
          & v1_funct_1(D) )
       => ! [E] : 
            ( ( v1_relat_1(E)
              & v1_funct_1(E) )
           => ( ( r1_tarski(C,k2_relat_1(k5_relat_1(D,E)))
                & v2_funct_1(E) )
             => r1_tarski(k10_relat_1(E,C),k2_relat_1(D)) ) ) ) ),
    introduced(definition,[new_symbol(c1_4__funct_3),file(funct_3,c1_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c1_4__funct_3)]).

fof(dh_c2_4__funct_3,definition,
    ( ( ( v1_relat_1(c2_4__funct_3)
        & v1_funct_1(c2_4__funct_3) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(c2_4__funct_3,A)))
              & v2_funct_1(A) )
           => r1_tarski(k10_relat_1(A,c1_4__funct_3),k2_relat_1(c2_4__funct_3)) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(B,C)))
                & v2_funct_1(C) )
             => r1_tarski(k10_relat_1(C,c1_4__funct_3),k2_relat_1(B)) ) ) ) ),
    introduced(definition,[new_symbol(c2_4__funct_3),file(funct_3,c2_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c2_4__funct_3)]).

fof(dh_c3_4__funct_3,definition,
    ( ( ( v1_relat_1(c3_4__funct_3)
        & v1_funct_1(c3_4__funct_3) )
     => ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3)))
          & v2_funct_1(c3_4__funct_3) )
       => r1_tarski(k10_relat_1(c3_4__funct_3,c1_4__funct_3),k2_relat_1(c2_4__funct_3)) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(c2_4__funct_3,A)))
            & v2_funct_1(A) )
         => r1_tarski(k10_relat_1(A,c1_4__funct_3),k2_relat_1(c2_4__funct_3)) ) ) ),
    introduced(definition,[new_symbol(c3_4__funct_3),file(funct_3,c3_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c3_4__funct_3)]).

fof(e1_4__funct_3,assumption,(
    r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3))) ),
    introduced(assumption,[file(funct_3,e1_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,e1_4__funct_3)]).

fof(e2_4__funct_3,assumption,(
    v2_funct_1(c3_4__funct_3) ),
    introduced(assumption,[file(funct_3,e2_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,e2_4__funct_3)]).

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(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_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_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_c1_4__funct_3,assumption,(
    $true ),
    introduced(assumption,[file(funct_3,c1_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c1_4__funct_3)]).

fof(dt_c2_4__funct_3,assumption,
    ( v1_relat_1(c2_4__funct_3)
    & v1_funct_1(c2_4__funct_3) ),
    introduced(assumption,[file(funct_3,c2_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c2_4__funct_3)]).

fof(dt_c3_4__funct_3,assumption,
    ( v1_relat_1(c3_4__funct_3)
    & v1_funct_1(c3_4__funct_3) ),
    introduced(assumption,[file(funct_3,c3_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c3_4__funct_3)]).

fof(dt_c4_4__funct_3,assumption,(
    $true ),
    introduced(assumption,[file(funct_3,c4_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c4_4__funct_3)]).

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_c4_4__funct_3,definition,
    ( ~ ( r2_hidden(c4_4__funct_3,k10_relat_1(c3_4__funct_3,c1_4__funct_3))
        & ~ r2_hidden(c4_4__funct_3,k2_relat_1(c2_4__funct_3)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k10_relat_1(c3_4__funct_3,c1_4__funct_3))
          & ~ r2_hidden(A,k2_relat_1(c2_4__funct_3)) ) ),
    introduced(definition,[new_symbol(c4_4__funct_3),file(funct_3,c4_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c4_4__funct_3)]).

fof(e3_4__funct_3,assumption,(
    r2_hidden(c4_4__funct_3,k10_relat_1(c3_4__funct_3,c1_4__funct_3)) ),
    introduced(assumption,[file(funct_3,e3_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,e3_4__funct_3)]).

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(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(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(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(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(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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

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(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(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_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_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_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(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(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(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(dh_c5_4__funct_3,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3)))
        & k1_funct_1(c3_4__funct_3,c4_4__funct_3) = k1_funct_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3),A) )
   => ( r2_hidden(c5_4__funct_3,k1_relat_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3)))
      & k1_funct_1(c3_4__funct_3,c4_4__funct_3) = k1_funct_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3),c5_4__funct_3) ) ),
    introduced(definition,[new_symbol(c5_4__funct_3),file(funct_3,c5_4__funct_3)]),
    [interesting(0.8),axiom,file(funct_3,c5_4__funct_3)]).

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

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_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(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_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(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(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(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(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(d13_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( r2_hidden(D,k1_relat_1(A))
                & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ),
    file(funct_1,d13_funct_1),
    [interesting(0.9),axiom,file(funct_1,d13_funct_1)]).

fof(e4_4__funct_3,plain,(
    r2_hidden(k1_funct_1(c3_4__funct_3,c4_4__funct_3),c1_4__funct_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,rc1_funct_1,t1_subset,t7_boole,e3_4__funct_3,d13_funct_1]),
    [interesting(0.8),file(funct_3,e4_4__funct_3),[file(funct_3,e4_4__funct_3)]]).

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(e5_4__funct_3,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3)))
      & k1_funct_1(c3_4__funct_3,c4_4__funct_3) = k1_funct_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3),A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3,e1_4__funct_3])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc1_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_relat_1,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k5_relat_1,dt_c1_4__funct_3,dt_c2_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,fc1_funct_1,rc1_funct_1,t1_subset,t3_subset,t7_boole,e4_4__funct_3,e1_4__funct_3,d5_funct_1]),
    [interesting(0.8),file(funct_3,e5_4__funct_3),[file(funct_3,e5_4__funct_3)]]).

fof(dt_c5_4__funct_3,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3,e1_4__funct_3])],[dh_c5_4__funct_3,e5_4__funct_3]),
    [interesting(0.8),file(funct_3,c5_4__funct_3),[file(funct_3,c5_4__funct_3)]]).

fof(e6_4__funct_3,plain,(
    r2_hidden(c5_4__funct_3,k1_relat_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3))) ),
    inference(consider,[status(thm),assumptions([dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3,e1_4__funct_3])],[dh_c5_4__funct_3,e5_4__funct_3]),
    [interesting(0.8),file(funct_3,e6_4__funct_3),[file(funct_3,e6_4__funct_3)]]).

fof(e7_4__funct_3,plain,(
    k1_funct_1(c3_4__funct_3,c4_4__funct_3) = k1_funct_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3),c5_4__funct_3) ),
    inference(consider,[status(thm),assumptions([dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3,e1_4__funct_3])],[dh_c5_4__funct_3,e5_4__funct_3]),
    [interesting(0.8),file(funct_3,e7_4__funct_3),[file(funct_3,e7_4__funct_3)]]).

fof(t21_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
          <=> ( r2_hidden(A,k1_relat_1(C))
              & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) ) ) ) ) ),
    file(funct_1,t21_funct_1),
    [interesting(0.9),axiom,file(funct_1,t21_funct_1)]).

fof(t22_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    [interesting(0.9),axiom,file(funct_1,t22_funct_1)]).

fof(e8_4__funct_3,plain,
    ( k1_funct_1(c3_4__funct_3,c4_4__funct_3) = k1_funct_1(c3_4__funct_3,k1_funct_1(c2_4__funct_3,c5_4__funct_3))
    & r2_hidden(c4_4__funct_3,k1_relat_1(c3_4__funct_3))
    & r2_hidden(k1_funct_1(c2_4__funct_3,c5_4__funct_3),k1_relat_1(c3_4__funct_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3,e1_4__funct_3])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k5_relat_1,dt_c1_4__funct_3,dt_c2_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,dt_c5_4__funct_3,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e3_4__funct_3,e6_4__funct_3,e7_4__funct_3,t21_funct_1,t22_funct_1,d13_funct_1]),
    [interesting(0.8),file(funct_3,e8_4__funct_3),[file(funct_3,e8_4__funct_3)]]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.9),axiom,file(funct_1,d8_funct_1)]).

fof(e9_4__funct_3,plain,
    ( c4_4__funct_3 = k1_funct_1(c2_4__funct_3,c5_4__funct_3)
    & r2_hidden(c5_4__funct_3,k1_relat_1(c2_4__funct_3)) ),
    inference(mizar_by,[status(thm),assumptions([e2_4__funct_3,dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3,e1_4__funct_3])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k5_relat_1,dt_c2_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,dt_c5_4__funct_3,fc1_funct_1,rc1_funct_1,rc3_funct_1,t1_subset,t7_boole,e8_4__funct_3,e2_4__funct_3,e6_4__funct_3,t21_funct_1,d8_funct_1]),
    [interesting(0.8),file(funct_3,e9_4__funct_3),[file(funct_3,e9_4__funct_3)]]).

fof(e10_4__funct_3,plain,(
    r2_hidden(c4_4__funct_3,k2_relat_1(c2_4__funct_3)) ),
    inference(mizar_by,[status(thm),assumptions([e2_4__funct_3,dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3,e1_4__funct_3])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c2_4__funct_3,dt_c4_4__funct_3,dt_c5_4__funct_3,rc1_funct_1,t1_subset,t7_boole,e9_4__funct_3,d5_funct_1]),
    [interesting(0.8),file(funct_3,e10_4__funct_3),[file(funct_3,e10_4__funct_3)]]).

fof(i6_4__funct_3,theorem,(
    $true ),
    introduced(tautology,[file(funct_3,i6_4__funct_3)]),
    [interesting(0.8),trivial,file(funct_3,i6_4__funct_3)]).

fof(i5_4__funct_3,plain,(
    r2_hidden(c4_4__funct_3,k2_relat_1(c2_4__funct_3)) ),
    inference(conclusion,[status(thm),assumptions([e2_4__funct_3,dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e3_4__funct_3,e1_4__funct_3])],[e10_4__funct_3,i6_4__funct_3]),
    [interesting(0.8),file(funct_3,i5_4__funct_3),[file(funct_3,i5_4__funct_3)]]).

fof(i4_4__funct_3,plain,(
    ~ ( r2_hidden(c4_4__funct_3,k10_relat_1(c3_4__funct_3,c1_4__funct_3))
      & ~ r2_hidden(c4_4__funct_3,k2_relat_1(c2_4__funct_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_4__funct_3,dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,dt_c4_4__funct_3,e1_4__funct_3]),discharge_asm(discharge,[e3_4__funct_3])],[e3_4__funct_3,i5_4__funct_3]),
    [interesting(0.8),file(funct_3,i4_4__funct_3),[file(funct_3,i4_4__funct_3)]]).

fof(i4_4_tmp__funct_3,plain,(
    ~ ( r2_hidden(c4_4__funct_3,k10_relat_1(c3_4__funct_3,c1_4__funct_3))
      & ~ r2_hidden(c4_4__funct_3,k2_relat_1(c2_4__funct_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_4__funct_3,dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,e1_4__funct_3]),discharge_asm(discharge,[dt_c4_4__funct_3])],[dt_c4_4__funct_3,i4_4__funct_3]),
    [interesting(0.8),i3_4__funct_3]).

fof(i3_4__funct_3,plain,(
    r1_tarski(k10_relat_1(c3_4__funct_3,c1_4__funct_3),k2_relat_1(c2_4__funct_3)) ),
    inference(let,[status(thm),assumptions([e2_4__funct_3,dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3,e1_4__funct_3])],[i4_4_tmp__funct_3,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k2_relat_1,dt_c1_4__funct_3,dt_c2_4__funct_3,dt_c3_4__funct_3,d3_tarski,dh_c4_4__funct_3]),
    [interesting(0.8),file(funct_3,i3_4__funct_3),[file(funct_3,i3_4__funct_3)]]).

fof(i2_4__funct_3,plain,
    ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3)))
      & v2_funct_1(c3_4__funct_3) )
   => r1_tarski(k10_relat_1(c3_4__funct_3,c1_4__funct_3),k2_relat_1(c2_4__funct_3)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_4__funct_3,dt_c1_4__funct_3,dt_c3_4__funct_3]),discharge_asm(discharge,[e1_4__funct_3,e2_4__funct_3])],[e1_4__funct_3,e2_4__funct_3,i3_4__funct_3]),
    [interesting(0.8),file(funct_3,i2_4__funct_3),[file(funct_3,i2_4__funct_3)]]).

fof(i2_4_tmp__funct_3,plain,
    ( ( v1_relat_1(c2_4__funct_3)
      & v1_funct_1(c2_4__funct_3)
      & v1_relat_1(c3_4__funct_3)
      & v1_funct_1(c3_4__funct_3) )
   => ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(c2_4__funct_3,c3_4__funct_3)))
        & v2_funct_1(c3_4__funct_3) )
     => r1_tarski(k10_relat_1(c3_4__funct_3,c1_4__funct_3),k2_relat_1(c2_4__funct_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__funct_3]),discharge_asm(discharge,[dt_c2_4__funct_3,dt_c3_4__funct_3])],[dt_c2_4__funct_3,dt_c3_4__funct_3,i2_4__funct_3]),
    [interesting(0.8),i1_4__funct_3]).

fof(i1_4__funct_3,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(A,B)))
              & v2_funct_1(B) )
           => r1_tarski(k10_relat_1(B,c1_4__funct_3),k2_relat_1(A)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__funct_3])],[i2_4_tmp__funct_3,dh_c2_4__funct_3,dh_c3_4__funct_3]),
    [interesting(0.8),file(funct_3,i1_4__funct_3),[file(funct_3,i1_4__funct_3)]]).

fof(i1_4_tmp__funct_3,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( r1_tarski(c1_4__funct_3,k2_relat_1(k5_relat_1(A,B)))
              & v2_funct_1(B) )
           => r1_tarski(k10_relat_1(B,c1_4__funct_3),k2_relat_1(A)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__funct_3])],[dt_c1_4__funct_3,i1_4__funct_3]),
    [interesting(1),t4_funct_3]).

fof(t4_funct_3,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))
              & v2_funct_1(C) )
           => r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__funct_3,dh_c1_4__funct_3]),
    [interesting(1),file(funct_3,t4_funct_3),[file(funct_3,t4_funct_3)]]).