% Mizar ND problem: t6_relat_1,relat_1,75,29 
fof(dh_c1_7__relat_1,definition,
    ( ! [A] : v1_relat_1(k2_zfmisc_1(c1_7__relat_1,A))
   => ! [B,C] : v1_relat_1(k2_zfmisc_1(B,C)) ),
    introduced(definition,[new_symbol(c1_7__relat_1),file(relat_1,c1_7__relat_1)]),
    [interesting(0.8),axiom,file(relat_1,c1_7__relat_1)]).

fof(dh_c2_7__relat_1,definition,
    ( v1_relat_1(k2_zfmisc_1(c1_7__relat_1,c2_7__relat_1))
   => ! [A] : v1_relat_1(k2_zfmisc_1(c1_7__relat_1,A)) ),
    introduced(definition,[new_symbol(c2_7__relat_1),file(relat_1,c2_7__relat_1)]),
    [interesting(0.8),axiom,file(relat_1,c2_7__relat_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_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_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_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_c1_7__relat_1,assumption,(
    $true ),
    introduced(assumption,[file(relat_1,c1_7__relat_1)]),
    [interesting(0.8),axiom,file(relat_1,c1_7__relat_1)]).

fof(dt_c2_7__relat_1,assumption,(
    $true ),
    introduced(assumption,[file(relat_1,c2_7__relat_1)]),
    [interesting(0.8),axiom,file(relat_1,c2_7__relat_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(d1_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
    <=> ! [B] : 
          ~ ( r2_hidden(B,A)
            & ! [C,D] : B != k4_tarski(C,D) ) ) ),
    file(relat_1,d1_relat_1),
    [interesting(0.9),axiom,file(relat_1,d1_relat_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(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(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(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_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(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(t102_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,k2_zfmisc_1(B,C))
        & ! [D,E] : k4_tarski(D,E) != A ) ),
    file(zfmisc_1,t102_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t102_zfmisc_1)]).

fof(e1_7__relat_1,plain,(
    ! [A] : 
      ~ ( r2_hidden(A,k2_zfmisc_1(c1_7__relat_1,c2_7__relat_1))
        & ! [B,C] : A != k4_tarski(B,C) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_7__relat_1,dt_c2_7__relat_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,fc2_subset_1,fc3_subset_1,fc4_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_7__relat_1,dt_c2_7__relat_1,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,t102_zfmisc_1]),
    [interesting(0.8),file(relat_1,e1_7__relat_1),[file(relat_1,e1_7__relat_1)]]).

fof(i3_7__relat_1,theorem,(
    $true ),
    introduced(tautology,[file(relat_1,i3_7__relat_1)]),
    [interesting(0.8),trivial,file(relat_1,i3_7__relat_1)]).

fof(i2_7__relat_1,plain,(
    v1_relat_1(k2_zfmisc_1(c1_7__relat_1,c2_7__relat_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_7__relat_1,dt_c2_7__relat_1])],[fc4_subset_1,rc1_relat_1,rc1_xboole_0,rc2_xboole_0,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_7__relat_1,dt_c2_7__relat_1,fc1_zfmisc_1,d1_relat_1,e1_7__relat_1,i3_7__relat_1]),
    [interesting(0.8),file(relat_1,i2_7__relat_1),[file(relat_1,i2_7__relat_1)]]).

fof(i2_7_tmp__relat_1,plain,(
    v1_relat_1(k2_zfmisc_1(c1_7__relat_1,c2_7__relat_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_7__relat_1]),discharge_asm(discharge,[dt_c2_7__relat_1])],[dt_c2_7__relat_1,i2_7__relat_1]),
    [interesting(0.8),i1_7__relat_1]).

fof(i1_7__relat_1,plain,(
    ! [A] : v1_relat_1(k2_zfmisc_1(c1_7__relat_1,A)) ),
    inference(let,[status(thm),assumptions([dt_c1_7__relat_1])],[i2_7_tmp__relat_1,dh_c2_7__relat_1]),
    [interesting(0.8),file(relat_1,i1_7__relat_1),[file(relat_1,i1_7__relat_1)]]).

fof(i1_7_tmp__relat_1,plain,(
    ! [A] : v1_relat_1(k2_zfmisc_1(c1_7__relat_1,A)) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_7__relat_1])],[dt_c1_7__relat_1,i1_7__relat_1]),
    [interesting(1),t6_relat_1]).

fof(t6_relat_1,theorem,(
    ! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) ),
    inference(let,[status(thm),assumptions([])],[i1_7_tmp__relat_1,dh_c1_7__relat_1]),
    [interesting(1),file(relat_1,t6_relat_1),[file(relat_1,t6_relat_1)]]).