% Mizar ND problem: t109_orders_1,orders_1,449,45 
fof(dh_c1_28__orders_1,definition,
    ( ( v1_relat_1(c1_28__orders_1)
     => ( v2_orders_1(c1_28__orders_1)
       => v1_orders_1(c1_28__orders_1) ) )
   => ! [A] : 
        ( v1_relat_1(A)
       => ( v2_orders_1(A)
         => v1_orders_1(A) ) ) ),
    introduced(definition,[new_symbol(c1_28__orders_1),file(orders_1,c1_28__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c1_28__orders_1)]).

fof(dt_c1_28__orders_1,assumption,(
    v1_relat_1(c1_28__orders_1) ),
    introduced(assumption,[file(orders_1,c1_28__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c1_28__orders_1)]).

fof(e1_28__orders_1,assumption,
    ( v1_relat_2(c1_28__orders_1)
    & v8_relat_2(c1_28__orders_1)
    & v4_relat_2(c1_28__orders_1) ),
    introduced(assumption,[file(orders_1,e1_28__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,e1_28__orders_1)]).

fof(d4_orders_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A) ) ) ) ),
    file(orders_1,d4_orders_1),
    [interesting(0.9),axiom,file(orders_1,d4_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(e2_28__orders_1,plain,
    ( v1_relat_2(c1_28__orders_1)
    & v8_relat_2(c1_28__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_28__orders_1,e1_28__orders_1])],[dt_c1_28__orders_1,e1_28__orders_1]),
    [interesting(0.8),file(orders_1,e2_28__orders_1),[file(orders_1,e2_28__orders_1)]]).

fof(i3_28__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i3_28__orders_1)]),
    [interesting(0.8),trivial,file(orders_1,i3_28__orders_1)]).

fof(i2_28__orders_1,plain,(
    v1_orders_1(c1_28__orders_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_28__orders_1,e1_28__orders_1])],[dt_c1_28__orders_1,d3_orders_1,e2_28__orders_1,i3_28__orders_1]),
    [interesting(0.8),file(orders_1,i2_28__orders_1),[file(orders_1,i2_28__orders_1)]]).

fof(i2_28_tmp__orders_1,plain,
    ( ( v1_relat_2(c1_28__orders_1)
      & v8_relat_2(c1_28__orders_1)
      & v4_relat_2(c1_28__orders_1) )
   => v1_orders_1(c1_28__orders_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_28__orders_1]),discharge_asm(discharge,[e1_28__orders_1])],[e1_28__orders_1,i2_28__orders_1]),
    [interesting(0.8),i1_28__orders_1]).

fof(i1_28__orders_1,plain,
    ( v2_orders_1(c1_28__orders_1)
   => v1_orders_1(c1_28__orders_1) ),
    inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_28__orders_1])],[i2_28_tmp__orders_1,d4_orders_1,dt_c1_28__orders_1]),
    [interesting(0.8),file(orders_1,i1_28__orders_1),[file(orders_1,i1_28__orders_1)]]).

fof(i1_28_tmp__orders_1,plain,
    ( v1_relat_1(c1_28__orders_1)
   => ( v2_orders_1(c1_28__orders_1)
     => v1_orders_1(c1_28__orders_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_28__orders_1])],[dt_c1_28__orders_1,i1_28__orders_1]),
    [interesting(1),t109_orders_1]).

fof(t109_orders_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_orders_1(A)
       => v1_orders_1(A) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_28_tmp__orders_1,dh_c1_28__orders_1]),
    [interesting(1),file(orders_1,t109_orders_1),[file(orders_1,t109_orders_1)]]).