% Mizar ND problem: t8_funct_4,funct_4,154,35 
fof(dh_c1_9__funct_4,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_hidden(c1_9__funct_4,k1_relat_1(A))
         => r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(A,c1_9__funct_4)),A) ) )
   => ! [B,C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ( r2_hidden(B,k1_relat_1(C))
         => r1_tarski(k2_funcop_1(k1_tarski(B),k1_funct_1(C,B)),C) ) ) ),
    introduced(definition,[new_symbol(c1_9__funct_4),file(funct_4,c1_9__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_9__funct_4)]).

fof(dh_c2_9__funct_4,definition,
    ( ( ( v1_relat_1(c2_9__funct_4)
        & v1_funct_1(c2_9__funct_4) )
     => ( r2_hidden(c1_9__funct_4,k1_relat_1(c2_9__funct_4))
       => r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c2_9__funct_4) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_hidden(c1_9__funct_4,k1_relat_1(A))
         => r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(A,c1_9__funct_4)),A) ) ) ),
    introduced(definition,[new_symbol(c2_9__funct_4),file(funct_4,c2_9__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_9__funct_4)]).

fof(e1_9__funct_4,assumption,(
    r2_hidden(c1_9__funct_4,k1_relat_1(c2_9__funct_4)) ),
    introduced(assumption,[file(funct_4,e1_9__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,e1_9__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(fc2_funcop_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc2_funcop_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(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(rc5_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc5_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_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_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(fc3_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc3_funcop_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(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(fc9_funcop_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc9_funcop_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(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_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

fof(dt_c1_9__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c1_9__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_9__funct_4)]).

fof(dt_c2_9__funct_4,assumption,
    ( v1_relat_1(c2_9__funct_4)
    & v1_funct_1(c2_9__funct_4) ),
    introduced(assumption,[file(funct_4,c2_9__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_9__funct_4)]).

fof(fc1_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc1_funcop_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(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(dh_c1_9_2__funct_4,definition,
    ( ( r2_hidden(c1_9_2__funct_4,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
     => k1_funct_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c1_9_2__funct_4) = k1_funct_1(c2_9__funct_4,c1_9_2__funct_4) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
       => k1_funct_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),A) = k1_funct_1(c2_9__funct_4,A) ) ),
    introduced(definition,[new_symbol(c1_9_2__funct_4),file(funct_4,c1_9_2__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,c1_9_2__funct_4)]).

fof(e1_9_2__funct_4,assumption,(
    r2_hidden(c1_9_2__funct_4,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)))) ),
    introduced(assumption,[file(funct_4,e1_9_2__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,e1_9_2__funct_4)]).

fof(dt_c1_9_2__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c1_9_2__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,c1_9_2__funct_4)]).

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

fof(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t19_funcop_1)]).

fof(e2_9__funct_4,plain,(
    k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))) = k1_tarski(c1_9__funct_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__funct_4,dt_c2_9__funct_4])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,rc1_funct_1,reflexivity_r1_tarski,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_c1_9__funct_4,dt_c2_9__funct_4,fc1_funcop_1,t3_subset,t19_funcop_1]),
    [interesting(0.8),file(funct_4,e2_9__funct_4),[file(funct_4,e2_9__funct_4)]]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t13_funcop_1)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e2_9_2__funct_4,plain,
    ( k1_funct_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c1_9_2__funct_4) = k1_funct_1(c2_9__funct_4,c1_9__funct_4)
    & c1_9_2__funct_4 = c1_9__funct_4 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_2__funct_4,e1_9_2__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_funcop_1,fc4_relat_1,rc3_funct_1,rc5_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc3_funcop_1,fc5_relat_1,fc7_relat_1,fc9_funcop_1,rc1_funct_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_k1_tarski,dt_k2_funcop_1,dt_c1_9__funct_4,dt_c1_9_2__funct_4,dt_c2_9__funct_4,fc1_funcop_1,t1_subset,t7_boole,e1_9_2__funct_4,e2_9__funct_4,t13_funcop_1,d1_tarski]),
    [interesting(0.65),file(funct_4,e2_9_2__funct_4),[file(funct_4,e2_9_2__funct_4)]]).

fof(e3_9_2__funct_4,plain,(
    k1_funct_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c1_9_2__funct_4) = k1_funct_1(c2_9__funct_4,c1_9_2__funct_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_2__funct_4,e1_9_2__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4])],[rc1_funct_1,dt_k1_funct_1,dt_k1_tarski,dt_k2_funcop_1,dt_c1_9__funct_4,dt_c1_9_2__funct_4,dt_c2_9__funct_4,fc1_funcop_1,e2_9_2__funct_4]),
    [interesting(0.65),file(funct_4,e3_9_2__funct_4),[file(funct_4,e3_9_2__funct_4)]]).

fof(i3_9_2__funct_4,theorem,(
    $true ),
    introduced(tautology,[file(funct_4,i3_9_2__funct_4)]),
    [interesting(0.65),trivial,file(funct_4,i3_9_2__funct_4)]).

fof(i2_9_2__funct_4,plain,(
    k1_funct_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c1_9_2__funct_4) = k1_funct_1(c2_9__funct_4,c1_9_2__funct_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9_2__funct_4,e1_9_2__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4])],[e3_9_2__funct_4,i3_9_2__funct_4]),
    [interesting(0.65),file(funct_4,i2_9_2__funct_4),[file(funct_4,i2_9_2__funct_4)]]).

fof(i1_9_2__funct_4,plain,
    ( r2_hidden(c1_9_2__funct_4,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
   => k1_funct_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c1_9_2__funct_4) = k1_funct_1(c2_9__funct_4,c1_9_2__funct_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9_2__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4]),discharge_asm(discharge,[e1_9_2__funct_4])],[e1_9_2__funct_4,i2_9_2__funct_4]),
    [interesting(0.65),file(funct_4,i1_9_2__funct_4),[file(funct_4,i1_9_2__funct_4)]]).

fof(i1_9_2_tmp__funct_4,plain,
    ( r2_hidden(c1_9_2__funct_4,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
   => k1_funct_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c1_9_2__funct_4) = k1_funct_1(c2_9__funct_4,c1_9_2__funct_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__funct_4,dt_c2_9__funct_4]),discharge_asm(discharge,[dt_c1_9_2__funct_4])],[dt_c1_9_2__funct_4,i1_9_2__funct_4]),
    [interesting(0.8),e4_9__funct_4]).

fof(e4_9__funct_4,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
     => k1_funct_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),A) = k1_funct_1(c2_9__funct_4,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__funct_4,dt_c2_9__funct_4])],[i1_9_2_tmp__funct_4,dh_c1_9_2__funct_4]),
    [interesting(0.8),file(funct_4,e4_9__funct_4),[file(funct_4,e4_9__funct_4)]]).

fof(dt_c1_9_1__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c1_9_1__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,c1_9_1__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_c1_9_1__funct_4,definition,
    ( ~ ( r2_hidden(c1_9_1__funct_4,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
        & ~ r2_hidden(c1_9_1__funct_4,k1_relat_1(c2_9__funct_4)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
          & ~ r2_hidden(A,k1_relat_1(c2_9__funct_4)) ) ),
    introduced(definition,[new_symbol(c1_9_1__funct_4),file(funct_4,c1_9_1__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,c1_9_1__funct_4)]).

fof(e1_9_1__funct_4,assumption,(
    r2_hidden(c1_9_1__funct_4,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)))) ),
    introduced(assumption,[file(funct_4,e1_9_1__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,e1_9_1__funct_4)]).

fof(e2_9_1__funct_4,plain,(
    r2_hidden(c1_9_1__funct_4,k1_relat_1(c2_9__funct_4)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9_1__funct_4,e1_9_1__funct_4,e1_9__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_funcop_1,fc4_relat_1,rc3_funct_1,rc5_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc3_funcop_1,fc5_relat_1,fc7_relat_1,fc9_funcop_1,rc1_funct_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_k1_tarski,dt_k2_funcop_1,dt_c1_9__funct_4,dt_c1_9_1__funct_4,dt_c2_9__funct_4,fc1_funcop_1,t1_subset,t7_boole,e1_9_1__funct_4,e1_9__funct_4,e2_9__funct_4,d1_tarski]),
    [interesting(0.65),file(funct_4,e2_9_1__funct_4),[file(funct_4,e2_9_1__funct_4)]]).

fof(i3_9_1__funct_4,theorem,(
    $true ),
    introduced(tautology,[file(funct_4,i3_9_1__funct_4)]),
    [interesting(0.65),trivial,file(funct_4,i3_9_1__funct_4)]).

fof(i2_9_1__funct_4,plain,(
    r2_hidden(c1_9_1__funct_4,k1_relat_1(c2_9__funct_4)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_9_1__funct_4,e1_9_1__funct_4,e1_9__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4])],[e2_9_1__funct_4,i3_9_1__funct_4]),
    [interesting(0.65),file(funct_4,i2_9_1__funct_4),[file(funct_4,i2_9_1__funct_4)]]).

fof(i1_9_1__funct_4,plain,(
    ~ ( r2_hidden(c1_9_1__funct_4,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
      & ~ r2_hidden(c1_9_1__funct_4,k1_relat_1(c2_9__funct_4)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9_1__funct_4,e1_9__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4]),discharge_asm(discharge,[e1_9_1__funct_4])],[e1_9_1__funct_4,i2_9_1__funct_4]),
    [interesting(0.65),file(funct_4,i1_9_1__funct_4),[file(funct_4,i1_9_1__funct_4)]]).

fof(i1_9_1_tmp__funct_4,plain,(
    ~ ( r2_hidden(c1_9_1__funct_4,k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))))
      & ~ r2_hidden(c1_9_1__funct_4,k1_relat_1(c2_9__funct_4)) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_9__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4]),discharge_asm(discharge,[dt_c1_9_1__funct_4])],[dt_c1_9_1__funct_4,i1_9_1__funct_4]),
    [interesting(0.8),e3_9__funct_4]).

fof(e3_9__funct_4,plain,(
    r1_tarski(k1_relat_1(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4))),k1_relat_1(c2_9__funct_4)) ),
    inference(let,[status(thm),assumptions([e1_9__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4])],[i1_9_1_tmp__funct_4,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_c1_9__funct_4,dt_c2_9__funct_4,fc1_funcop_1,d3_tarski,dh_c1_9_1__funct_4]),
    [interesting(0.8),file(funct_4,e3_9__funct_4),[file(funct_4,e3_9__funct_4)]]).

fof(t8_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    [interesting(0.9),axiom,file(grfunc_1,t8_grfunc_1)]).

fof(e5_9__funct_4,plain,(
    r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c2_9__funct_4) ),
    inference(mizar_by,[status(thm),assumptions([e1_9__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4])],[rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc2_funcop_1,fc4_relat_1,rc3_funct_1,rc5_funct_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc3_funcop_1,fc5_relat_1,fc7_relat_1,fc9_funcop_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_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_k1_tarski,dt_k2_funcop_1,dt_c1_9__funct_4,dt_c2_9__funct_4,fc1_funcop_1,rc1_funct_1,t1_subset,t3_subset,t7_boole,e4_9__funct_4,e3_9__funct_4,t8_grfunc_1]),
    [interesting(0.8),file(funct_4,e5_9__funct_4),[file(funct_4,e5_9__funct_4)]]).

fof(i4_9__funct_4,theorem,(
    $true ),
    introduced(tautology,[file(funct_4,i4_9__funct_4)]),
    [interesting(0.8),trivial,file(funct_4,i4_9__funct_4)]).

fof(i3_9__funct_4,plain,(
    r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c2_9__funct_4) ),
    inference(conclusion,[status(thm),assumptions([e1_9__funct_4,dt_c1_9__funct_4,dt_c2_9__funct_4])],[e5_9__funct_4,i4_9__funct_4]),
    [interesting(0.8),file(funct_4,i3_9__funct_4),[file(funct_4,i3_9__funct_4)]]).

fof(i2_9__funct_4,plain,
    ( r2_hidden(c1_9__funct_4,k1_relat_1(c2_9__funct_4))
   => r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c2_9__funct_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__funct_4,dt_c2_9__funct_4]),discharge_asm(discharge,[e1_9__funct_4])],[e1_9__funct_4,i3_9__funct_4]),
    [interesting(0.8),file(funct_4,i2_9__funct_4),[file(funct_4,i2_9__funct_4)]]).

fof(i2_9_tmp__funct_4,plain,
    ( ( v1_relat_1(c2_9__funct_4)
      & v1_funct_1(c2_9__funct_4) )
   => ( r2_hidden(c1_9__funct_4,k1_relat_1(c2_9__funct_4))
     => r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(c2_9__funct_4,c1_9__funct_4)),c2_9__funct_4) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__funct_4]),discharge_asm(discharge,[dt_c2_9__funct_4])],[dt_c2_9__funct_4,i2_9__funct_4]),
    [interesting(0.8),i1_9__funct_4]).

fof(i1_9__funct_4,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r2_hidden(c1_9__funct_4,k1_relat_1(A))
       => r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(A,c1_9__funct_4)),A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__funct_4])],[i2_9_tmp__funct_4,dh_c2_9__funct_4]),
    [interesting(0.8),file(funct_4,i1_9__funct_4),[file(funct_4,i1_9__funct_4)]]).

fof(i1_9_tmp__funct_4,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r2_hidden(c1_9__funct_4,k1_relat_1(A))
       => r1_tarski(k2_funcop_1(k1_tarski(c1_9__funct_4),k1_funct_1(A,c1_9__funct_4)),A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_9__funct_4])],[dt_c1_9__funct_4,i1_9__funct_4]),
    [interesting(1),t8_funct_4]).

fof(t8_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_9_tmp__funct_4,dh_c1_9__funct_4]),
    [interesting(1),file(funct_4,t8_funct_4),[file(funct_4,t8_funct_4)]]).