% Mizar ND problem: t1_funct_4,funct_4,48,77 
fof(dh_c1_3__funct_4,definition,
    ( ~ ( ! [A] : 
            ~ ( r2_hidden(A,c1_3__funct_4)
              & ! [B,C] : A != k4_tarski(B,C) )
        & ! [A,B] : ~ r1_tarski(c1_3__funct_4,k2_zfmisc_1(A,B)) )
   => ! [D] : 
        ~ ( ! [E] : 
              ~ ( r2_hidden(E,D)
                & ! [F,G] : E != k4_tarski(F,G) )
          & ! [E,F] : ~ r1_tarski(D,k2_zfmisc_1(E,F)) ) ),
    introduced(definition,[new_symbol(c1_3__funct_4),file(funct_4,c1_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_3__funct_4)]).

fof(e1_3__funct_4,assumption,(
    ! [A] : 
      ~ ( r2_hidden(A,c1_3__funct_4)
        & ! [B,C] : A != k4_tarski(B,C) ) ),
    introduced(assumption,[file(funct_4,e1_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,e1_3__funct_4)]).

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

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_c1_3__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c1_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_3__funct_4)]).

fof(dh_c2_3__funct_4,definition,
    ( ? [A] : 
      ! [B] : 
        ( r2_hidden(B,A)
      <=> ( r2_hidden(B,k3_tarski(k3_tarski(c1_3__funct_4)))
          & ? [C] : r2_hidden(k4_tarski(B,C),c1_3__funct_4) ) )
   => ! [D] : 
        ( r2_hidden(D,c2_3__funct_4)
      <=> ( r2_hidden(D,k3_tarski(k3_tarski(c1_3__funct_4)))
          & ? [E] : r2_hidden(k4_tarski(D,E),c1_3__funct_4) ) ) ),
    introduced(definition,[new_symbol(c2_3__funct_4),file(funct_4,c2_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_3__funct_4)]).

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(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(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(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(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(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(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_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(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_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

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

fof(fc1_zfmisc_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,fc1_zfmisc_1)]).

fof(s1_xboole_0__e2_3__funct_4,theorem,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(A)))
        & ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ),
    file(funct_4,s1_xboole_0__e2_3__funct_4),
    [interesting(0.9),axiom,file(funct_4,s1_xboole_0__e2_3__funct_4)]).

fof(e2_3__funct_4,plain,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,k3_tarski(k3_tarski(c1_3__funct_4)))
        & ? [C] : r2_hidden(k4_tarski(B,C),c1_3__funct_4) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_3__funct_4])],[rc3_funct_1,cc2_funct_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_3__funct_4,fc1_zfmisc_1,s1_xboole_0__e2_3__funct_4]),
    [interesting(0.8),file(funct_4,e2_3__funct_4),[file(funct_4,e2_3__funct_4)]]).

fof(dt_c2_3__funct_4,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_4])],[dh_c2_3__funct_4,e2_3__funct_4]),
    [interesting(0.8),file(funct_4,c2_3__funct_4),[file(funct_4,c2_3__funct_4)]]).

fof(dh_c3_3__funct_4,definition,
    ( ? [A] : 
      ! [B] : 
        ( r2_hidden(B,A)
      <=> ( r2_hidden(B,k3_tarski(k3_tarski(c1_3__funct_4)))
          & ? [C] : r2_hidden(k4_tarski(C,B),c1_3__funct_4) ) )
   => ! [D] : 
        ( r2_hidden(D,c3_3__funct_4)
      <=> ( r2_hidden(D,k3_tarski(k3_tarski(c1_3__funct_4)))
          & ? [E] : r2_hidden(k4_tarski(E,D),c1_3__funct_4) ) ) ),
    introduced(definition,[new_symbol(c3_3__funct_4),file(funct_4,c3_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c3_3__funct_4)]).

fof(s1_xboole_0__e4_3__funct_4,theorem,(
    ! [A] : 
    ? [B] : 
    ! [C] : 
      ( r2_hidden(C,B)
    <=> ( r2_hidden(C,k3_tarski(k3_tarski(A)))
        & ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ),
    file(funct_4,s1_xboole_0__e4_3__funct_4),
    [interesting(0.9),axiom,file(funct_4,s1_xboole_0__e4_3__funct_4)]).

fof(e4_3__funct_4,plain,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,k3_tarski(k3_tarski(c1_3__funct_4)))
        & ? [C] : r2_hidden(k4_tarski(C,B),c1_3__funct_4) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_3__funct_4])],[rc3_funct_1,cc2_funct_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_3__funct_4,fc1_zfmisc_1,s1_xboole_0__e4_3__funct_4]),
    [interesting(0.8),file(funct_4,e4_3__funct_4),[file(funct_4,e4_3__funct_4)]]).

fof(dt_c3_3__funct_4,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_4])],[dh_c3_3__funct_4,e4_3__funct_4]),
    [interesting(0.8),file(funct_4,c3_3__funct_4),[file(funct_4,c3_3__funct_4)]]).

fof(dt_c4_3__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c4_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c4_3__funct_4)]).

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_3__funct_4,definition,
    ( ~ ( r2_hidden(c4_3__funct_4,c1_3__funct_4)
        & ~ r2_hidden(c4_3__funct_4,k2_zfmisc_1(c2_3__funct_4,c3_3__funct_4)) )
   => ! [A] : 
        ~ ( r2_hidden(A,c1_3__funct_4)
          & ~ r2_hidden(A,k2_zfmisc_1(c2_3__funct_4,c3_3__funct_4)) ) ),
    introduced(definition,[new_symbol(c4_3__funct_4),file(funct_4,c4_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c4_3__funct_4)]).

fof(e6_3__funct_4,assumption,(
    r2_hidden(c4_3__funct_4,c1_3__funct_4) ),
    introduced(assumption,[file(funct_4,e6_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,e6_3__funct_4)]).

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(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_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(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(dh_c5_3__funct_4,definition,
    ( ? [A,B] : c4_3__funct_4 = k4_tarski(A,B)
   => ? [C] : c4_3__funct_4 = k4_tarski(c5_3__funct_4,C) ),
    introduced(definition,[new_symbol(c5_3__funct_4),file(funct_4,c5_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c5_3__funct_4)]).

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(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(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(e7_3__funct_4,plain,(
    ? [A,B] : c4_3__funct_4 = k4_tarski(A,B) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e6_3__funct_4,e1_3__funct_4])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_3__funct_4,dt_c4_3__funct_4,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,e6_3__funct_4,e1_3__funct_4]),
    [interesting(0.8),file(funct_4,e7_3__funct_4),[file(funct_4,e7_3__funct_4)]]).

fof(dt_c5_3__funct_4,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e6_3__funct_4,e1_3__funct_4])],[dh_c5_3__funct_4,e7_3__funct_4]),
    [interesting(0.8),file(funct_4,c5_3__funct_4),[file(funct_4,c5_3__funct_4)]]).

fof(dh_c6_3__funct_4,definition,
    ( ? [A] : c4_3__funct_4 = k4_tarski(c5_3__funct_4,A)
   => c4_3__funct_4 = k4_tarski(c5_3__funct_4,c6_3__funct_4) ),
    introduced(definition,[new_symbol(c6_3__funct_4),file(funct_4,c6_3__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c6_3__funct_4)]).

fof(dt_c6_3__funct_4,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e6_3__funct_4,e1_3__funct_4])],[dh_c5_3__funct_4,dh_c6_3__funct_4,e7_3__funct_4]),
    [interesting(0.8),file(funct_4,c6_3__funct_4),[file(funct_4,c6_3__funct_4)]]).

fof(e8_3__funct_4,plain,(
    c4_3__funct_4 = k4_tarski(c5_3__funct_4,c6_3__funct_4) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e6_3__funct_4,e1_3__funct_4])],[dh_c5_3__funct_4,dh_c6_3__funct_4,e7_3__funct_4]),
    [interesting(0.8),file(funct_4,e8_3__funct_4),[file(funct_4,e8_3__funct_4)]]).

fof(l1_funct_4,plain,(
    ! [A,B,C] : 
      ( r2_hidden(k4_tarski(A,B),C)
     => ( r2_hidden(A,k3_tarski(k3_tarski(C)))
        & r2_hidden(B,k3_tarski(k3_tarski(C))) ) ) ),
    file(funct_4,l1_funct_4),
    [interesting(0.9),axiom,file(funct_4,l1_funct_4)]).

fof(e9_3__funct_4,plain,
    ( r2_hidden(c6_3__funct_4,k3_tarski(k3_tarski(c1_3__funct_4)))
    & r2_hidden(c5_3__funct_4,k3_tarski(k3_tarski(c1_3__funct_4))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e6_3__funct_4,e1_3__funct_4])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_3__funct_4,dt_c4_3__funct_4,dt_c5_3__funct_4,dt_c6_3__funct_4,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,e6_3__funct_4,e8_3__funct_4,l1_funct_4]),
    [interesting(0.8),file(funct_4,e9_3__funct_4),[file(funct_4,e9_3__funct_4)]]).

fof(e3_3__funct_4,plain,(
    ! [A] : 
      ( r2_hidden(A,c2_3__funct_4)
    <=> ( r2_hidden(A,k3_tarski(k3_tarski(c1_3__funct_4)))
        & ? [B] : r2_hidden(k4_tarski(A,B),c1_3__funct_4) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_4])],[dh_c2_3__funct_4,e2_3__funct_4]),
    [interesting(0.8),file(funct_4,e3_3__funct_4),[file(funct_4,e3_3__funct_4)]]).

fof(e5_3__funct_4,plain,(
    ! [A] : 
      ( r2_hidden(A,c3_3__funct_4)
    <=> ( r2_hidden(A,k3_tarski(k3_tarski(c1_3__funct_4)))
        & ? [B] : r2_hidden(k4_tarski(B,A),c1_3__funct_4) ) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__funct_4])],[dh_c3_3__funct_4,e4_3__funct_4]),
    [interesting(0.8),file(funct_4,e5_3__funct_4),[file(funct_4,e5_3__funct_4)]]).

fof(e10_3__funct_4,plain,
    ( r2_hidden(c6_3__funct_4,c3_3__funct_4)
    & r2_hidden(c5_3__funct_4,c2_3__funct_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e6_3__funct_4,e1_3__funct_4])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_3__funct_4,dt_c2_3__funct_4,dt_c3_3__funct_4,dt_c4_3__funct_4,dt_c5_3__funct_4,dt_c6_3__funct_4,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,e9_3__funct_4,e3_3__funct_4,e5_3__funct_4,e6_3__funct_4,e8_3__funct_4]),
    [interesting(0.8),file(funct_4,e10_3__funct_4),[file(funct_4,e10_3__funct_4)]]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t106_zfmisc_1)]).

fof(e11_3__funct_4,plain,(
    r2_hidden(c4_3__funct_4,k2_zfmisc_1(c2_3__funct_4,c3_3__funct_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e6_3__funct_4,e1_3__funct_4])],[rc3_funct_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k4_tarski,dt_c2_3__funct_4,dt_c3_3__funct_4,dt_c4_3__funct_4,dt_c5_3__funct_4,dt_c6_3__funct_4,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,e10_3__funct_4,e8_3__funct_4,t106_zfmisc_1]),
    [interesting(0.8),file(funct_4,e11_3__funct_4),[file(funct_4,e11_3__funct_4)]]).

fof(i7_3__funct_4,theorem,(
    $true ),
    introduced(tautology,[file(funct_4,i7_3__funct_4)]),
    [interesting(0.8),trivial,file(funct_4,i7_3__funct_4)]).

fof(i6_3__funct_4,plain,(
    r2_hidden(c4_3__funct_4,k2_zfmisc_1(c2_3__funct_4,c3_3__funct_4)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e6_3__funct_4,e1_3__funct_4])],[e11_3__funct_4,i7_3__funct_4]),
    [interesting(0.8),file(funct_4,i6_3__funct_4),[file(funct_4,i6_3__funct_4)]]).

fof(i5_3__funct_4,plain,(
    ~ ( r2_hidden(c4_3__funct_4,c1_3__funct_4)
      & ~ r2_hidden(c4_3__funct_4,k2_zfmisc_1(c2_3__funct_4,c3_3__funct_4)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__funct_4,dt_c4_3__funct_4,e1_3__funct_4]),discharge_asm(discharge,[e6_3__funct_4])],[e6_3__funct_4,i6_3__funct_4]),
    [interesting(0.8),file(funct_4,i5_3__funct_4),[file(funct_4,i5_3__funct_4)]]).

fof(i5_3_tmp__funct_4,plain,(
    ~ ( r2_hidden(c4_3__funct_4,c1_3__funct_4)
      & ~ r2_hidden(c4_3__funct_4,k2_zfmisc_1(c2_3__funct_4,c3_3__funct_4)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__funct_4,e1_3__funct_4]),discharge_asm(discharge,[dt_c4_3__funct_4])],[dt_c4_3__funct_4,i5_3__funct_4]),
    [interesting(0.8),i4_3__funct_4]).

fof(i4_3__funct_4,plain,(
    r1_tarski(c1_3__funct_4,k2_zfmisc_1(c2_3__funct_4,c3_3__funct_4)) ),
    inference(let,[status(thm),assumptions([dt_c1_3__funct_4,e1_3__funct_4])],[i5_3_tmp__funct_4,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_c1_3__funct_4,dt_c2_3__funct_4,dt_c3_3__funct_4,d3_tarski,dh_c4_3__funct_4]),
    [interesting(0.8),file(funct_4,i4_3__funct_4),[file(funct_4,i4_3__funct_4)]]).

fof(i3_3__funct_4,plain,(
    ? [A] : r1_tarski(c1_3__funct_4,k2_zfmisc_1(c2_3__funct_4,A)) ),
    inference(take,[status(thm),assumptions([dt_c1_3__funct_4,e1_3__funct_4])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,dt_c1_3__funct_4,dt_c2_3__funct_4,dt_c3_3__funct_4,i4_3__funct_4]),
    [interesting(0.8),file(funct_4,i3_3__funct_4),[file(funct_4,i3_3__funct_4)]]).

fof(i2_3__funct_4,plain,(
    ? [A,B] : r1_tarski(c1_3__funct_4,k2_zfmisc_1(A,B)) ),
    inference(take,[status(thm),assumptions([dt_c1_3__funct_4,e1_3__funct_4])],[reflexivity_r1_tarski,dt_k2_zfmisc_1,dt_c1_3__funct_4,dt_c2_3__funct_4,i3_3__funct_4]),
    [interesting(0.8),file(funct_4,i2_3__funct_4),[file(funct_4,i2_3__funct_4)]]).

fof(i1_3__funct_4,plain,(
    ~ ( ! [A] : 
          ~ ( r2_hidden(A,c1_3__funct_4)
            & ! [B,C] : A != k4_tarski(B,C) )
      & ! [A,B] : ~ r1_tarski(c1_3__funct_4,k2_zfmisc_1(A,B)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__funct_4]),discharge_asm(discharge,[e1_3__funct_4])],[e1_3__funct_4,i2_3__funct_4]),
    [interesting(0.8),file(funct_4,i1_3__funct_4),[file(funct_4,i1_3__funct_4)]]).

fof(i1_3_tmp__funct_4,plain,(
    ~ ( ! [A] : 
          ~ ( r2_hidden(A,c1_3__funct_4)
            & ! [B,C] : A != k4_tarski(B,C) )
      & ! [A,B] : ~ r1_tarski(c1_3__funct_4,k2_zfmisc_1(A,B)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__funct_4])],[dt_c1_3__funct_4,i1_3__funct_4]),
    [interesting(1),t1_funct_4]).

fof(t1_funct_4,theorem,(
    ! [A] : 
      ~ ( ! [B] : 
            ~ ( r2_hidden(B,A)
              & ! [C,D] : B != k4_tarski(C,D) )
        & ! [B,C] : ~ r1_tarski(A,k2_zfmisc_1(B,C)) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__funct_4,dh_c1_3__funct_4]),
    [interesting(1),file(funct_4,t1_funct_4),[file(funct_4,t1_funct_4)]]).