% Mizar ND problem: t129_orders_1,orders_1,653,35 
fof(dh_c1_47__orders_1,definition,
    ( ( v1_relat_1(c1_47__orders_1)
     => ! [A] : 
          ( r1_orders_1(c1_47__orders_1,A)
         => v1_orders_1(k2_wellord1(c1_47__orders_1,A)) ) )
   => ! [B] : 
        ( v1_relat_1(B)
       => ! [C] : 
            ( r1_orders_1(B,C)
           => v1_orders_1(k2_wellord1(B,C)) ) ) ),
    introduced(definition,[new_symbol(c1_47__orders_1),file(orders_1,c1_47__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c1_47__orders_1)]).

fof(dh_c2_47__orders_1,definition,
    ( ( r1_orders_1(c1_47__orders_1,c2_47__orders_1)
     => v1_orders_1(k2_wellord1(c1_47__orders_1,c2_47__orders_1)) )
   => ! [A] : 
        ( r1_orders_1(c1_47__orders_1,A)
       => v1_orders_1(k2_wellord1(c1_47__orders_1,A)) ) ),
    introduced(definition,[new_symbol(c2_47__orders_1),file(orders_1,c2_47__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c2_47__orders_1)]).

fof(dt_k2_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k2_wellord1(A,B)) ) ),
    file(wellord1,k2_wellord1),
    [interesting(0.9),axiom,file(wellord1,k2_wellord1)]).

fof(dt_c1_47__orders_1,assumption,(
    v1_relat_1(c1_47__orders_1) ),
    introduced(assumption,[file(orders_1,c1_47__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c1_47__orders_1)]).

fof(dt_c2_47__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c2_47__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c2_47__orders_1)]).

fof(e1_47__orders_1,assumption,
    ( r1_relat_2(c1_47__orders_1,c2_47__orders_1)
    & r8_relat_2(c1_47__orders_1,c2_47__orders_1) ),
    introduced(assumption,[file(orders_1,e1_47__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,e1_47__orders_1)]).

fof(d6_orders_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_orders_1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B) ) ) ) ),
    file(orders_1,d6_orders_1),
    [interesting(0.9),axiom,file(orders_1,d6_orders_1)]).

fof(d3_orders_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A) ) ) ) ),
    file(orders_1,d3_orders_1),
    [interesting(0.9),axiom,file(orders_1,d3_orders_1)]).

fof(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

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_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(d6_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B)) ) ),
    file(wellord1,d6_wellord1),
    [interesting(0.9),axiom,file(wellord1,d6_wellord1)]).

fof(l142_orders_1,plain,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
         => v1_relat_2(k2_wellord1(A,B)) ) ) ),
    file(orders_1,l142_orders_1),
    [interesting(0.9),axiom,file(orders_1,l142_orders_1)]).

fof(l143_orders_1,plain,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
         => v8_relat_2(k2_wellord1(A,B)) ) ) ),
    file(orders_1,l143_orders_1),
    [interesting(0.9),axiom,file(orders_1,l143_orders_1)]).

fof(e2_47__orders_1,plain,
    ( v1_relat_2(k2_wellord1(c1_47__orders_1,c2_47__orders_1))
    & v8_relat_2(k2_wellord1(c1_47__orders_1,c2_47__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_47__orders_1,dt_c2_47__orders_1,e1_47__orders_1])],[commutativity_k3_xboole_0,idempotence_k3_xboole_0,dt_k2_zfmisc_1,dt_k3_xboole_0,dt_k2_wellord1,dt_c1_47__orders_1,dt_c2_47__orders_1,d6_wellord1,e1_47__orders_1,l142_orders_1,l143_orders_1]),
    [interesting(0.8),file(orders_1,e2_47__orders_1),[file(orders_1,e2_47__orders_1)]]).

fof(i4_47__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i4_47__orders_1)]),
    [interesting(0.8),trivial,file(orders_1,i4_47__orders_1)]).

fof(i3_47__orders_1,plain,(
    v1_orders_1(k2_wellord1(c1_47__orders_1,c2_47__orders_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_47__orders_1,dt_c2_47__orders_1,e1_47__orders_1])],[dt_k2_wellord1,dt_c1_47__orders_1,dt_c2_47__orders_1,d3_orders_1,e2_47__orders_1,i4_47__orders_1]),
    [interesting(0.8),file(orders_1,i3_47__orders_1),[file(orders_1,i3_47__orders_1)]]).

fof(i3_47_tmp__orders_1,plain,
    ( ( r1_relat_2(c1_47__orders_1,c2_47__orders_1)
      & r8_relat_2(c1_47__orders_1,c2_47__orders_1) )
   => v1_orders_1(k2_wellord1(c1_47__orders_1,c2_47__orders_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_47__orders_1,dt_c2_47__orders_1]),discharge_asm(discharge,[e1_47__orders_1])],[e1_47__orders_1,i3_47__orders_1]),
    [interesting(0.8),i2_47__orders_1]).

fof(i2_47__orders_1,plain,
    ( r1_orders_1(c1_47__orders_1,c2_47__orders_1)
   => v1_orders_1(k2_wellord1(c1_47__orders_1,c2_47__orders_1)) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_47__orders_1,dt_c2_47__orders_1])],[i3_47_tmp__orders_1,d6_orders_1,dt_k2_wellord1,dt_c1_47__orders_1,dt_c2_47__orders_1]),
    [interesting(0.8),file(orders_1,i2_47__orders_1),[file(orders_1,i2_47__orders_1)]]).

fof(i2_47_tmp__orders_1,plain,
    ( r1_orders_1(c1_47__orders_1,c2_47__orders_1)
   => v1_orders_1(k2_wellord1(c1_47__orders_1,c2_47__orders_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_47__orders_1]),discharge_asm(discharge,[dt_c2_47__orders_1])],[dt_c2_47__orders_1,i2_47__orders_1]),
    [interesting(0.8),i1_47__orders_1]).

fof(i1_47__orders_1,plain,(
    ! [A] : 
      ( r1_orders_1(c1_47__orders_1,A)
     => v1_orders_1(k2_wellord1(c1_47__orders_1,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_47__orders_1])],[i2_47_tmp__orders_1,dh_c2_47__orders_1]),
    [interesting(0.8),file(orders_1,i1_47__orders_1),[file(orders_1,i1_47__orders_1)]]).

fof(i1_47_tmp__orders_1,plain,
    ( v1_relat_1(c1_47__orders_1)
   => ! [A] : 
        ( r1_orders_1(c1_47__orders_1,A)
       => v1_orders_1(k2_wellord1(c1_47__orders_1,A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_47__orders_1])],[dt_c1_47__orders_1,i1_47__orders_1]),
    [interesting(1),t129_orders_1]).

fof(t129_orders_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_orders_1(A,B)
         => v1_orders_1(k2_wellord1(A,B)) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_47_tmp__orders_1,dh_c1_47__orders_1]),
    [interesting(1),file(orders_1,t129_orders_1),[file(orders_1,t129_orders_1)]]).