% Mizar ND problem: t11_binari_6,binari_6,106,55 
fof(dh_c1_11__binari_6,definition,
    ( ( v2_margrel1(c1_11__binari_6)
     => ! [A] : 
          ( v2_margrel1(A)
         => ! [B] : 
              ( v2_margrel1(B)
             => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(A,B)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(A),B)),k1_binarith(k9_margrel1(B),A)) ) ) )
   => ! [C] : 
        ( v2_margrel1(C)
       => ! [D] : 
            ( v2_margrel1(D)
           => ! [E] : 
                ( v2_margrel1(E)
               => k10_margrel1(C,k2_bvfunc_1(D,E)) = k10_margrel1(k10_margrel1(C,k1_binarith(k9_margrel1(D),E)),k1_binarith(k9_margrel1(E),D)) ) ) ) ),
    introduced(definition,[new_symbol(c1_11__binari_6),file(binari_6,c1_11__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c1_11__binari_6)]).

fof(dh_c2_11__binari_6,definition,
    ( ( v2_margrel1(c2_11__binari_6)
     => ! [A] : 
          ( v2_margrel1(A)
         => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,A)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),A)),k1_binarith(k9_margrel1(A),c2_11__binari_6)) ) )
   => ! [B] : 
        ( v2_margrel1(B)
       => ! [C] : 
            ( v2_margrel1(C)
           => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(B,C)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(B),C)),k1_binarith(k9_margrel1(C),B)) ) ) ),
    introduced(definition,[new_symbol(c2_11__binari_6),file(binari_6,c2_11__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c2_11__binari_6)]).

fof(dh_c3_11__binari_6,definition,
    ( ( v2_margrel1(c3_11__binari_6)
     => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,c3_11__binari_6)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),c3_11__binari_6)),k1_binarith(k9_margrel1(c3_11__binari_6),c2_11__binari_6)) )
   => ! [A] : 
        ( v2_margrel1(A)
       => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,A)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),A)),k1_binarith(k9_margrel1(A),c2_11__binari_6)) ) ),
    introduced(definition,[new_symbol(c3_11__binari_6),file(binari_6,c3_11__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c3_11__binari_6)]).

fof(commutativity_k1_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k1_binarith(A,B) = k1_binarith(B,A) ) ),
    file(binarith,k1_binarith),
    [interesting(0.9),axiom,file(binarith,k1_binarith)]).

fof(commutativity_k2_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k2_binarith(A,B) = k2_binarith(B,A) ) ),
    file(binarith,k2_binarith),
    [interesting(0.9),axiom,file(binarith,k2_binarith)]).

fof(involutiveness_k9_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,k9_margrel1),
    [interesting(0.9),axiom,file(margrel1,k9_margrel1)]).

fof(dt_k1_binarith,axiom,(
    $true ),
    file(binarith,k1_binarith),
    [interesting(0.9),axiom,file(binarith,k1_binarith)]).

fof(dt_k2_binarith,axiom,(
    $true ),
    file(binarith,k2_binarith),
    [interesting(0.9),axiom,file(binarith,k2_binarith)]).

fof(dt_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_margrel1),
    [interesting(0.9),axiom,file(margrel1,k9_margrel1)]).

fof(fc1_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_binarith(A,B)) ) ),
    file(binarith,fc1_binarith),
    [interesting(0.9),axiom,file(binarith,fc1_binarith)]).

fof(fc2_binarith,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k2_binarith(A,B)) ) ),
    file(binarith,fc2_binarith),
    [interesting(0.9),axiom,file(binarith,fc2_binarith)]).

fof(fc4_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,fc4_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc4_margrel1)]).

fof(commutativity_k10_margrel1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k10_margrel1(A,B) = k10_margrel1(B,A) ) ),
    file(margrel1,k10_margrel1),
    [interesting(0.9),axiom,file(margrel1,k10_margrel1)]).

fof(commutativity_k2_bvfunc_1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k2_bvfunc_1(A,B) = k2_bvfunc_1(B,A) ) ),
    file(bvfunc_1,k2_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k2_bvfunc_1)]).

fof(dt_k10_margrel1,axiom,(
    $true ),
    file(margrel1,k10_margrel1),
    [interesting(0.9),axiom,file(margrel1,k10_margrel1)]).

fof(dt_k1_bvfunc_1,axiom,(
    $true ),
    file(bvfunc_1,k1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k1_bvfunc_1)]).

fof(dt_k2_bvfunc_1,axiom,(
    $true ),
    file(bvfunc_1,k2_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k2_bvfunc_1)]).

fof(dt_c1_11__binari_6,assumption,(
    v2_margrel1(c1_11__binari_6) ),
    introduced(assumption,[file(binari_6,c1_11__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c1_11__binari_6)]).

fof(dt_c2_11__binari_6,assumption,(
    v2_margrel1(c2_11__binari_6) ),
    introduced(assumption,[file(binari_6,c2_11__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c2_11__binari_6)]).

fof(dt_c3_11__binari_6,assumption,(
    v2_margrel1(c3_11__binari_6) ),
    introduced(assumption,[file(binari_6,c3_11__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c3_11__binari_6)]).

fof(cc1_bvfunc_1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(bvfunc_1,cc1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,cc1_bvfunc_1)]).

fof(fc1_bvfunc_1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_bvfunc_1(A,B)) ) ),
    file(bvfunc_1,fc1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,fc1_bvfunc_1)]).

fof(fc2_bvfunc_1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k2_bvfunc_1(A,B)) ) ),
    file(bvfunc_1,fc2_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,fc2_bvfunc_1)]).

fof(fc5_margrel1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k10_margrel1(A,B)) ) ),
    file(margrel1,fc5_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc5_margrel1)]).

fof(rc2_margrel1,theorem,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc2_margrel1)]).

fof(d1_bvfunc_1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,B) = k1_binarith(k9_margrel1(A),B) ) ) ),
    file(bvfunc_1,d1_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,d1_bvfunc_1)]).

fof(d2_bvfunc_1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k2_bvfunc_1(A,B) = k9_margrel1(k2_binarith(A,B)) ) ) ),
    file(bvfunc_1,d2_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,d2_bvfunc_1)]).

fof(t23_binari_5,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k2_bvfunc_1(A,B) = k10_margrel1(k1_bvfunc_1(A,B),k1_bvfunc_1(B,A)) ) ) ),
    file(binari_5,t23_binari_5),
    [interesting(0.9),axiom,file(binari_5,t23_binari_5)]).

fof(e1_11_1__binari_6,plain,(
    k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,c3_11__binari_6)) = k10_margrel1(c1_11__binari_6,k10_margrel1(k1_bvfunc_1(c2_11__binari_6,c3_11__binari_6),k1_bvfunc_1(c3_11__binari_6,c2_11__binari_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_11__binari_6,dt_c2_11__binari_6,dt_c3_11__binari_6])],[commutativity_k1_binarith,commutativity_k2_binarith,involutiveness_k9_margrel1,dt_k1_binarith,dt_k2_binarith,dt_k9_margrel1,fc1_binarith,fc2_binarith,fc4_margrel1,commutativity_k10_margrel1,commutativity_k2_bvfunc_1,dt_k10_margrel1,dt_k1_bvfunc_1,dt_k2_bvfunc_1,dt_c1_11__binari_6,dt_c2_11__binari_6,dt_c3_11__binari_6,cc1_bvfunc_1,fc1_bvfunc_1,fc2_bvfunc_1,fc5_margrel1,rc2_margrel1,d1_bvfunc_1,d2_bvfunc_1,t23_binari_5]),
    [interesting(0.65),file(binari_6,e1_11_1__binari_6),[file(binari_6,e1_11_1__binari_6)]]).

fof(t52_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k10_margrel1(A,k10_margrel1(B,C)) = k10_margrel1(k10_margrel1(A,B),C) ) ) ) ),
    file(margrel1,t52_margrel1),
    [interesting(0.9),axiom,file(margrel1,t52_margrel1)]).

fof(e2_11_1__binari_6,plain,(
    k10_margrel1(c1_11__binari_6,k10_margrel1(k1_bvfunc_1(c2_11__binari_6,c3_11__binari_6),k1_bvfunc_1(c3_11__binari_6,c2_11__binari_6))) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),c3_11__binari_6)),k1_binarith(k9_margrel1(c3_11__binari_6),c2_11__binari_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_11__binari_6,dt_c2_11__binari_6,dt_c3_11__binari_6])],[commutativity_k10_margrel1,commutativity_k1_binarith,involutiveness_k9_margrel1,dt_k10_margrel1,dt_k1_binarith,dt_k1_bvfunc_1,dt_k9_margrel1,dt_c1_11__binari_6,dt_c2_11__binari_6,dt_c3_11__binari_6,cc1_bvfunc_1,fc1_binarith,fc1_bvfunc_1,fc4_margrel1,fc5_margrel1,rc2_margrel1,d1_bvfunc_1,t52_margrel1]),
    [interesting(0.65),file(binari_6,e2_11_1__binari_6),[file(binari_6,e2_11_1__binari_6)]]).

fof(e1_11__binari_6,plain,(
    k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,c3_11__binari_6)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),c3_11__binari_6)),k1_binarith(k9_margrel1(c3_11__binari_6),c2_11__binari_6)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_11__binari_6,dt_c2_11__binari_6,dt_c3_11__binari_6])],[e1_11_1__binari_6,e2_11_1__binari_6]),
    [interesting(0.8),file(binari_6,e1_11__binari_6),[file(binari_6,e1_11__binari_6)]]).

fof(i4_11__binari_6,theorem,(
    $true ),
    introduced(tautology,[file(binari_6,i4_11__binari_6)]),
    [interesting(0.8),trivial,file(binari_6,i4_11__binari_6)]).

fof(i3_11__binari_6,plain,(
    k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,c3_11__binari_6)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),c3_11__binari_6)),k1_binarith(k9_margrel1(c3_11__binari_6),c2_11__binari_6)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_11__binari_6,dt_c2_11__binari_6,dt_c3_11__binari_6])],[e1_11__binari_6,i4_11__binari_6]),
    [interesting(0.8),file(binari_6,i3_11__binari_6),[file(binari_6,i3_11__binari_6)]]).

fof(i3_11_tmp__binari_6,plain,
    ( v2_margrel1(c3_11__binari_6)
   => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,c3_11__binari_6)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),c3_11__binari_6)),k1_binarith(k9_margrel1(c3_11__binari_6),c2_11__binari_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_11__binari_6,dt_c2_11__binari_6]),discharge_asm(discharge,[dt_c3_11__binari_6])],[dt_c3_11__binari_6,i3_11__binari_6]),
    [interesting(0.8),i2_11__binari_6]).

fof(i2_11__binari_6,plain,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,A)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),A)),k1_binarith(k9_margrel1(A),c2_11__binari_6)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_11__binari_6,dt_c2_11__binari_6])],[i3_11_tmp__binari_6,dh_c3_11__binari_6]),
    [interesting(0.8),file(binari_6,i2_11__binari_6),[file(binari_6,i2_11__binari_6)]]).

fof(i2_11_tmp__binari_6,plain,
    ( v2_margrel1(c2_11__binari_6)
   => ! [A] : 
        ( v2_margrel1(A)
       => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(c2_11__binari_6,A)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(c2_11__binari_6),A)),k1_binarith(k9_margrel1(A),c2_11__binari_6)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_11__binari_6]),discharge_asm(discharge,[dt_c2_11__binari_6])],[dt_c2_11__binari_6,i2_11__binari_6]),
    [interesting(0.8),i1_11__binari_6]).

fof(i1_11__binari_6,plain,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(A,B)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(A),B)),k1_binarith(k9_margrel1(B),A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_11__binari_6])],[i2_11_tmp__binari_6,dh_c2_11__binari_6]),
    [interesting(0.8),file(binari_6,i1_11__binari_6),[file(binari_6,i1_11__binari_6)]]).

fof(i1_11_tmp__binari_6,plain,
    ( v2_margrel1(c1_11__binari_6)
   => ! [A] : 
        ( v2_margrel1(A)
       => ! [B] : 
            ( v2_margrel1(B)
           => k10_margrel1(c1_11__binari_6,k2_bvfunc_1(A,B)) = k10_margrel1(k10_margrel1(c1_11__binari_6,k1_binarith(k9_margrel1(A),B)),k1_binarith(k9_margrel1(B),A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_11__binari_6])],[dt_c1_11__binari_6,i1_11__binari_6]),
    [interesting(1),t11_binari_6]).

fof(t11_binari_6,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k10_margrel1(A,k2_bvfunc_1(B,C)) = k10_margrel1(k10_margrel1(A,k1_binarith(k9_margrel1(B),C)),k1_binarith(k9_margrel1(C),B)) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_11_tmp__binari_6,dh_c1_11__binari_6]),
    [interesting(1),file(binari_6,t11_binari_6),[file(binari_6,t11_binari_6)]]).