% Mizar ND problem: t8_relset_1,relset_1,72,48 
fof(dh_c1_6__relset_1,definition,
    ( ! [A,B,C] : 
        ( ( r2_hidden(B,c1_6__relset_1)
          & r2_hidden(C,A) )
       => m2_relset_1(k1_tarski(k4_tarski(B,C)),c1_6__relset_1,A) )
   => ! [D,E,F,G] : 
        ( ( r2_hidden(F,D)
          & r2_hidden(G,E) )
       => m2_relset_1(k1_tarski(k4_tarski(F,G)),D,E) ) ),
    introduced(definition,[new_symbol(c1_6__relset_1),file(relset_1,c1_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,c1_6__relset_1)]).

fof(dh_c2_6__relset_1,definition,
    ( ! [A,B] : 
        ( ( r2_hidden(A,c1_6__relset_1)
          & r2_hidden(B,c2_6__relset_1) )
       => m2_relset_1(k1_tarski(k4_tarski(A,B)),c1_6__relset_1,c2_6__relset_1) )
   => ! [C,D,E] : 
        ( ( r2_hidden(D,c1_6__relset_1)
          & r2_hidden(E,C) )
       => m2_relset_1(k1_tarski(k4_tarski(D,E)),c1_6__relset_1,C) ) ),
    introduced(definition,[new_symbol(c2_6__relset_1),file(relset_1,c2_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,c2_6__relset_1)]).

fof(dh_c3_6__relset_1,definition,
    ( ! [A] : 
        ( ( r2_hidden(c3_6__relset_1,c1_6__relset_1)
          & r2_hidden(A,c2_6__relset_1) )
       => m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,A)),c1_6__relset_1,c2_6__relset_1) )
   => ! [B,C] : 
        ( ( r2_hidden(B,c1_6__relset_1)
          & r2_hidden(C,c2_6__relset_1) )
       => m2_relset_1(k1_tarski(k4_tarski(B,C)),c1_6__relset_1,c2_6__relset_1) ) ),
    introduced(definition,[new_symbol(c3_6__relset_1),file(relset_1,c3_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,c3_6__relset_1)]).

fof(dh_c4_6__relset_1,definition,
    ( ( ( r2_hidden(c3_6__relset_1,c1_6__relset_1)
        & r2_hidden(c4_6__relset_1,c2_6__relset_1) )
     => m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,c4_6__relset_1)),c1_6__relset_1,c2_6__relset_1) )
   => ! [A] : 
        ( ( r2_hidden(c3_6__relset_1,c1_6__relset_1)
          & r2_hidden(A,c2_6__relset_1) )
       => m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,A)),c1_6__relset_1,c2_6__relset_1) ) ),
    introduced(definition,[new_symbol(c4_6__relset_1),file(relset_1,c4_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,c4_6__relset_1)]).

fof(e1_6__relset_1,assumption,
    ( r2_hidden(c3_6__relset_1,c1_6__relset_1)
    & r2_hidden(c4_6__relset_1,c2_6__relset_1) ),
    introduced(assumption,[file(relset_1,e1_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,e1_6__relset_1)]).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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(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(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(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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

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(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_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(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(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(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(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_c1_6__relset_1,assumption,(
    $true ),
    introduced(assumption,[file(relset_1,c1_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,c1_6__relset_1)]).

fof(dt_c2_6__relset_1,assumption,(
    $true ),
    introduced(assumption,[file(relset_1,c2_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,c2_6__relset_1)]).

fof(dt_c3_6__relset_1,assumption,(
    $true ),
    introduced(assumption,[file(relset_1,c3_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,c3_6__relset_1)]).

fof(dt_c4_6__relset_1,assumption,(
    $true ),
    introduced(assumption,[file(relset_1,c4_6__relset_1)]),
    [interesting(0.8),axiom,file(relset_1,c4_6__relset_1)]).

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(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(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(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(e2_6__relset_1,plain,(
    r2_hidden(k4_tarski(c3_6__relset_1,c4_6__relset_1),k2_zfmisc_1(c1_6__relset_1,c2_6__relset_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1,dt_c4_6__relset_1,e1_6__relset_1])],[dt_k1_xboole_0,fc1_xboole_0,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1,dt_c4_6__relset_1,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,e1_6__relset_1,t106_zfmisc_1]),
    [interesting(0.8),file(relset_1,e2_6__relset_1),[file(relset_1,e2_6__relset_1)]]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t37_zfmisc_1)]).

fof(e3_6__relset_1,plain,(
    r1_tarski(k1_tarski(k4_tarski(c3_6__relset_1,c4_6__relset_1)),k2_zfmisc_1(c1_6__relset_1,c2_6__relset_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1,dt_c4_6__relset_1,e1_6__relset_1])],[dt_k1_xboole_0,fc1_xboole_0,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,cc1_relset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1,dt_c4_6__relset_1,fc1_zfmisc_1,t1_subset,t3_subset,t7_boole,d5_tarski,e2_6__relset_1,t37_zfmisc_1]),
    [interesting(0.8),file(relset_1,e3_6__relset_1),[file(relset_1,e3_6__relset_1)]]).

fof(d1_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
    <=> r1_tarski(C,k2_zfmisc_1(A,B)) ) ),
    file(relset_1,d1_relset_1),
    [interesting(0.9),axiom,file(relset_1,d1_relset_1)]).

fof(e4_6__relset_1,plain,(
    m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,c4_6__relset_1)),c1_6__relset_1,c2_6__relset_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1,dt_c4_6__relset_1,e1_6__relset_1])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,cc1_relset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_relset_1,dt_m2_relset_1,dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1,dt_c4_6__relset_1,fc1_zfmisc_1,t3_subset,d5_tarski,e3_6__relset_1,d1_relset_1]),
    [interesting(0.8),file(relset_1,e4_6__relset_1),[file(relset_1,e4_6__relset_1)]]).

fof(i6_6__relset_1,theorem,(
    $true ),
    introduced(tautology,[file(relset_1,i6_6__relset_1)]),
    [interesting(0.8),trivial,file(relset_1,i6_6__relset_1)]).

fof(i5_6__relset_1,plain,(
    m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,c4_6__relset_1)),c1_6__relset_1,c2_6__relset_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1,dt_c4_6__relset_1,e1_6__relset_1])],[e4_6__relset_1,i6_6__relset_1]),
    [interesting(0.8),file(relset_1,i5_6__relset_1),[file(relset_1,i5_6__relset_1)]]).

fof(i4_6__relset_1,plain,
    ( ( r2_hidden(c3_6__relset_1,c1_6__relset_1)
      & r2_hidden(c4_6__relset_1,c2_6__relset_1) )
   => m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,c4_6__relset_1)),c1_6__relset_1,c2_6__relset_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1,dt_c4_6__relset_1]),discharge_asm(discharge,[e1_6__relset_1])],[e1_6__relset_1,i5_6__relset_1]),
    [interesting(0.8),file(relset_1,i4_6__relset_1),[file(relset_1,i4_6__relset_1)]]).

fof(i4_6_tmp__relset_1,plain,
    ( ( r2_hidden(c3_6__relset_1,c1_6__relset_1)
      & r2_hidden(c4_6__relset_1,c2_6__relset_1) )
   => m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,c4_6__relset_1)),c1_6__relset_1,c2_6__relset_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1]),discharge_asm(discharge,[dt_c4_6__relset_1])],[dt_c4_6__relset_1,i4_6__relset_1]),
    [interesting(0.8),i3_6__relset_1]).

fof(i3_6__relset_1,plain,(
    ! [A] : 
      ( ( r2_hidden(c3_6__relset_1,c1_6__relset_1)
        & r2_hidden(A,c2_6__relset_1) )
     => m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,A)),c1_6__relset_1,c2_6__relset_1) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1,dt_c3_6__relset_1])],[i4_6_tmp__relset_1,dh_c4_6__relset_1]),
    [interesting(0.8),file(relset_1,i3_6__relset_1),[file(relset_1,i3_6__relset_1)]]).

fof(i3_6_tmp__relset_1,plain,(
    ! [A] : 
      ( ( r2_hidden(c3_6__relset_1,c1_6__relset_1)
        & r2_hidden(A,c2_6__relset_1) )
     => m2_relset_1(k1_tarski(k4_tarski(c3_6__relset_1,A)),c1_6__relset_1,c2_6__relset_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1]),discharge_asm(discharge,[dt_c3_6__relset_1])],[dt_c3_6__relset_1,i3_6__relset_1]),
    [interesting(0.8),i2_6__relset_1]).

fof(i2_6__relset_1,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,c1_6__relset_1)
        & r2_hidden(B,c2_6__relset_1) )
     => m2_relset_1(k1_tarski(k4_tarski(A,B)),c1_6__relset_1,c2_6__relset_1) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__relset_1,dt_c2_6__relset_1])],[i3_6_tmp__relset_1,dh_c3_6__relset_1]),
    [interesting(0.8),file(relset_1,i2_6__relset_1),[file(relset_1,i2_6__relset_1)]]).

fof(i2_6_tmp__relset_1,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,c1_6__relset_1)
        & r2_hidden(B,c2_6__relset_1) )
     => m2_relset_1(k1_tarski(k4_tarski(A,B)),c1_6__relset_1,c2_6__relset_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__relset_1]),discharge_asm(discharge,[dt_c2_6__relset_1])],[dt_c2_6__relset_1,i2_6__relset_1]),
    [interesting(0.8),i1_6__relset_1]).

fof(i1_6__relset_1,plain,(
    ! [A,B,C] : 
      ( ( r2_hidden(B,c1_6__relset_1)
        & r2_hidden(C,A) )
     => m2_relset_1(k1_tarski(k4_tarski(B,C)),c1_6__relset_1,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__relset_1])],[i2_6_tmp__relset_1,dh_c2_6__relset_1]),
    [interesting(0.8),file(relset_1,i1_6__relset_1),[file(relset_1,i1_6__relset_1)]]).

fof(i1_6_tmp__relset_1,plain,(
    ! [A,B,C] : 
      ( ( r2_hidden(B,c1_6__relset_1)
        & r2_hidden(C,A) )
     => m2_relset_1(k1_tarski(k4_tarski(B,C)),c1_6__relset_1,A) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__relset_1])],[dt_c1_6__relset_1,i1_6__relset_1]),
    [interesting(1),t8_relset_1]).

fof(t8_relset_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r2_hidden(C,A)
        & r2_hidden(D,B) )
     => m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__relset_1,dh_c1_6__relset_1]),
    [interesting(1),file(relset_1,t8_relset_1),[file(relset_1,t8_relset_1)]]).