% Mizar ND problem: t5_funct_4,funct_4,121,37 
fof(dh_c1_6__funct_4,definition,
    ( ! [A,B] : 
        ( r1_tarski(c1_6__funct_4,A)
       => r1_tarski(k2_funcop_1(c1_6__funct_4,B),k2_funcop_1(A,B)) )
   => ! [C,D,E] : 
        ( r1_tarski(C,D)
       => r1_tarski(k2_funcop_1(C,E),k2_funcop_1(D,E)) ) ),
    introduced(definition,[new_symbol(c1_6__funct_4),file(funct_4,c1_6__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_6__funct_4)]).

fof(dh_c2_6__funct_4,definition,
    ( ! [A] : 
        ( r1_tarski(c1_6__funct_4,c2_6__funct_4)
       => r1_tarski(k2_funcop_1(c1_6__funct_4,A),k2_funcop_1(c2_6__funct_4,A)) )
   => ! [B,C] : 
        ( r1_tarski(c1_6__funct_4,B)
       => r1_tarski(k2_funcop_1(c1_6__funct_4,C),k2_funcop_1(B,C)) ) ),
    introduced(definition,[new_symbol(c2_6__funct_4),file(funct_4,c2_6__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_6__funct_4)]).

fof(dh_c3_6__funct_4,definition,
    ( ( r1_tarski(c1_6__funct_4,c2_6__funct_4)
     => r1_tarski(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),k2_funcop_1(c2_6__funct_4,c3_6__funct_4)) )
   => ! [A] : 
        ( r1_tarski(c1_6__funct_4,c2_6__funct_4)
       => r1_tarski(k2_funcop_1(c1_6__funct_4,A),k2_funcop_1(c2_6__funct_4,A)) ) ),
    introduced(definition,[new_symbol(c3_6__funct_4),file(funct_4,c3_6__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c3_6__funct_4)]).

fof(e1_6__funct_4,assumption,(
    r1_tarski(c1_6__funct_4,c2_6__funct_4) ),
    introduced(assumption,[file(funct_4,e1_6__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,e1_6__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_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

fof(dt_c1_6__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c1_6__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c1_6__funct_4)]).

fof(dt_c2_6__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c2_6__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c2_6__funct_4)]).

fof(dt_c3_6__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c3_6__funct_4)]),
    [interesting(0.8),axiom,file(funct_4,c3_6__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_6_1__funct_4,definition,
    ( ( r2_hidden(c1_6_1__funct_4,k1_relat_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4)))
     => k1_funct_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) = k1_funct_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4)))
       => k1_funct_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),A) = k1_funct_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4),A) ) ),
    introduced(definition,[new_symbol(c1_6_1__funct_4),file(funct_4,c1_6_1__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,c1_6_1__funct_4)]).

fof(e1_6_1__funct_4,assumption,(
    r2_hidden(c1_6_1__funct_4,k1_relat_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4))) ),
    introduced(assumption,[file(funct_4,e1_6_1__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,e1_6_1__funct_4)]).

fof(dt_c1_6_1__funct_4,assumption,(
    $true ),
    introduced(assumption,[file(funct_4,c1_6_1__funct_4)]),
    [interesting(0.65),axiom,file(funct_4,c1_6_1__funct_4)]).

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

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_6__funct_4,plain,
    ( k1_relat_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4)) = c1_6__funct_4
    & k1_relat_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4)) = c2_6__funct_4 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,rc1_funct_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4,fc1_funcop_1,t3_subset,t19_funcop_1]),
    [interesting(0.8),file(funct_4,e2_6__funct_4),[file(funct_4,e2_6__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(e2_6_1__funct_4,plain,
    ( k1_funct_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) = c3_6__funct_4
    & k1_funct_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) = c3_6__funct_4 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__funct_4,e1_6_1__funct_4,e1_6__funct_4,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__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_funct_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_k2_funcop_1,dt_c1_6__funct_4,dt_c1_6_1__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4,fc1_funcop_1,t1_subset,t3_subset,t7_boole,e1_6_1__funct_4,e1_6__funct_4,e2_6__funct_4,t13_funcop_1]),
    [interesting(0.65),file(funct_4,e2_6_1__funct_4),[file(funct_4,e2_6_1__funct_4)]]).

fof(e3_6_1__funct_4,plain,(
    k1_funct_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) = k1_funct_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__funct_4,e1_6_1__funct_4,e1_6__funct_4,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4])],[rc1_funct_1,dt_k1_funct_1,dt_k2_funcop_1,dt_c1_6__funct_4,dt_c1_6_1__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4,fc1_funcop_1,e2_6_1__funct_4]),
    [interesting(0.65),file(funct_4,e3_6_1__funct_4),[file(funct_4,e3_6_1__funct_4)]]).

fof(i3_6_1__funct_4,theorem,(
    $true ),
    introduced(tautology,[file(funct_4,i3_6_1__funct_4)]),
    [interesting(0.65),trivial,file(funct_4,i3_6_1__funct_4)]).

fof(i2_6_1__funct_4,plain,(
    k1_funct_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) = k1_funct_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6_1__funct_4,e1_6_1__funct_4,e1_6__funct_4,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4])],[e3_6_1__funct_4,i3_6_1__funct_4]),
    [interesting(0.65),file(funct_4,i2_6_1__funct_4),[file(funct_4,i2_6_1__funct_4)]]).

fof(i1_6_1__funct_4,plain,
    ( r2_hidden(c1_6_1__funct_4,k1_relat_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4)))
   => k1_funct_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) = k1_funct_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6_1__funct_4,e1_6__funct_4,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4]),discharge_asm(discharge,[e1_6_1__funct_4])],[e1_6_1__funct_4,i2_6_1__funct_4]),
    [interesting(0.65),file(funct_4,i1_6_1__funct_4),[file(funct_4,i1_6_1__funct_4)]]).

fof(i1_6_1_tmp__funct_4,plain,
    ( r2_hidden(c1_6_1__funct_4,k1_relat_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4)))
   => k1_funct_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) = k1_funct_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4),c1_6_1__funct_4) ),
    inference(discharge_asm,[status(thm),assumptions([e1_6__funct_4,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4]),discharge_asm(discharge,[dt_c1_6_1__funct_4])],[dt_c1_6_1__funct_4,i1_6_1__funct_4]),
    [interesting(0.8),e3_6__funct_4]).

fof(e3_6__funct_4,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4)))
     => k1_funct_1(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),A) = k1_funct_1(k2_funcop_1(c2_6__funct_4,c3_6__funct_4),A) ) ),
    inference(let,[status(thm),assumptions([e1_6__funct_4,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4])],[i1_6_1_tmp__funct_4,dh_c1_6_1__funct_4]),
    [interesting(0.8),file(funct_4,e3_6__funct_4),[file(funct_4,e3_6__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(e4_6__funct_4,plain,(
    r1_tarski(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),k2_funcop_1(c2_6__funct_4,c3_6__funct_4)) ),
    inference(mizar_by,[status(thm),assumptions([e1_6__funct_4,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__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_k2_funcop_1,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4,fc1_funcop_1,rc1_funct_1,t1_subset,t3_subset,t7_boole,e3_6__funct_4,e1_6__funct_4,e2_6__funct_4,t8_grfunc_1]),
    [interesting(0.8),file(funct_4,e4_6__funct_4),[file(funct_4,e4_6__funct_4)]]).

fof(i5_6__funct_4,theorem,(
    $true ),
    introduced(tautology,[file(funct_4,i5_6__funct_4)]),
    [interesting(0.8),trivial,file(funct_4,i5_6__funct_4)]).

fof(i4_6__funct_4,plain,(
    r1_tarski(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),k2_funcop_1(c2_6__funct_4,c3_6__funct_4)) ),
    inference(conclusion,[status(thm),assumptions([e1_6__funct_4,dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4])],[e4_6__funct_4,i5_6__funct_4]),
    [interesting(0.8),file(funct_4,i4_6__funct_4),[file(funct_4,i4_6__funct_4)]]).

fof(i3_6__funct_4,plain,
    ( r1_tarski(c1_6__funct_4,c2_6__funct_4)
   => r1_tarski(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),k2_funcop_1(c2_6__funct_4,c3_6__funct_4)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__funct_4,dt_c2_6__funct_4,dt_c3_6__funct_4]),discharge_asm(discharge,[e1_6__funct_4])],[e1_6__funct_4,i4_6__funct_4]),
    [interesting(0.8),file(funct_4,i3_6__funct_4),[file(funct_4,i3_6__funct_4)]]).

fof(i3_6_tmp__funct_4,plain,
    ( r1_tarski(c1_6__funct_4,c2_6__funct_4)
   => r1_tarski(k2_funcop_1(c1_6__funct_4,c3_6__funct_4),k2_funcop_1(c2_6__funct_4,c3_6__funct_4)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__funct_4,dt_c2_6__funct_4]),discharge_asm(discharge,[dt_c3_6__funct_4])],[dt_c3_6__funct_4,i3_6__funct_4]),
    [interesting(0.8),i2_6__funct_4]).

fof(i2_6__funct_4,plain,(
    ! [A] : 
      ( r1_tarski(c1_6__funct_4,c2_6__funct_4)
     => r1_tarski(k2_funcop_1(c1_6__funct_4,A),k2_funcop_1(c2_6__funct_4,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__funct_4,dt_c2_6__funct_4])],[i3_6_tmp__funct_4,dh_c3_6__funct_4]),
    [interesting(0.8),file(funct_4,i2_6__funct_4),[file(funct_4,i2_6__funct_4)]]).

fof(i2_6_tmp__funct_4,plain,(
    ! [A] : 
      ( r1_tarski(c1_6__funct_4,c2_6__funct_4)
     => r1_tarski(k2_funcop_1(c1_6__funct_4,A),k2_funcop_1(c2_6__funct_4,A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__funct_4]),discharge_asm(discharge,[dt_c2_6__funct_4])],[dt_c2_6__funct_4,i2_6__funct_4]),
    [interesting(0.8),i1_6__funct_4]).

fof(i1_6__funct_4,plain,(
    ! [A,B] : 
      ( r1_tarski(c1_6__funct_4,A)
     => r1_tarski(k2_funcop_1(c1_6__funct_4,B),k2_funcop_1(A,B)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__funct_4])],[i2_6_tmp__funct_4,dh_c2_6__funct_4]),
    [interesting(0.8),file(funct_4,i1_6__funct_4),[file(funct_4,i1_6__funct_4)]]).

fof(i1_6_tmp__funct_4,plain,(
    ! [A,B] : 
      ( r1_tarski(c1_6__funct_4,A)
     => r1_tarski(k2_funcop_1(c1_6__funct_4,B),k2_funcop_1(A,B)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__funct_4])],[dt_c1_6__funct_4,i1_6__funct_4]),
    [interesting(1),t5_funct_4]).

fof(t5_funct_4,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k2_funcop_1(A,C),k2_funcop_1(B,C)) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__funct_4,dh_c1_6__funct_4]),
    [interesting(1),file(funct_4,t5_funct_4),[file(funct_4,t5_funct_4)]]).