% Mizar ND problem: t4_binari_6,binari_6,43,33 
fof(dh_c1_4__binari_6,definition,
    ( ( v2_margrel1(c1_4__binari_6)
     => ! [A] : 
          ( v2_margrel1(A)
         => k9_margrel1(k1_bvfunc_1(c1_4__binari_6,A)) = k10_margrel1(c1_4__binari_6,k9_margrel1(A)) ) )
   => ! [B] : 
        ( v2_margrel1(B)
       => ! [C] : 
            ( v2_margrel1(C)
           => k9_margrel1(k1_bvfunc_1(B,C)) = k10_margrel1(B,k9_margrel1(C)) ) ) ),
    introduced(definition,[new_symbol(c1_4__binari_6),file(binari_6,c1_4__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c1_4__binari_6)]).

fof(dh_c2_4__binari_6,definition,
    ( ( v2_margrel1(c2_4__binari_6)
     => k9_margrel1(k1_bvfunc_1(c1_4__binari_6,c2_4__binari_6)) = k10_margrel1(c1_4__binari_6,k9_margrel1(c2_4__binari_6)) )
   => ! [A] : 
        ( v2_margrel1(A)
       => k9_margrel1(k1_bvfunc_1(c1_4__binari_6,A)) = k10_margrel1(c1_4__binari_6,k9_margrel1(A)) ) ),
    introduced(definition,[new_symbol(c2_4__binari_6),file(binari_6,c2_4__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c2_4__binari_6)]).

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_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(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_k10_margrel1,axiom,(
    $true ),
    file(margrel1,k10_margrel1),
    [interesting(0.9),axiom,file(margrel1,k10_margrel1)]).

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

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_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(dt_c1_4__binari_6,assumption,(
    v2_margrel1(c1_4__binari_6) ),
    introduced(assumption,[file(binari_6,c1_4__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c1_4__binari_6)]).

fof(dt_c2_4__binari_6,assumption,(
    v2_margrel1(c2_4__binari_6) ),
    introduced(assumption,[file(binari_6,c2_4__binari_6)]),
    [interesting(0.8),axiom,file(binari_6,c2_4__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_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(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(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(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(t10_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k9_margrel1(k1_binarith(A,B)) = k10_margrel1(k9_margrel1(A),k9_margrel1(B)) ) ) ),
    file(binarith,t10_binarith),
    [interesting(0.9),axiom,file(binarith,t10_binarith)]).

fof(e1_4_1__binari_6,plain,(
    k9_margrel1(k1_bvfunc_1(c1_4__binari_6,c2_4__binari_6)) = k10_margrel1(k9_margrel1(k9_margrel1(c1_4__binari_6)),k9_margrel1(c2_4__binari_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__binari_6,dt_c2_4__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_4__binari_6,dt_c2_4__binari_6,cc1_bvfunc_1,fc1_binarith,fc1_bvfunc_1,fc4_margrel1,fc5_margrel1,rc2_margrel1,d1_bvfunc_1,t10_binarith]),
    [interesting(0.65),file(binari_6,e1_4_1__binari_6),[file(binari_6,e1_4_1__binari_6)]]).

fof(t40_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,t40_margrel1),
    [interesting(0.9),axiom,file(margrel1,t40_margrel1)]).

fof(e2_4_1__binari_6,plain,(
    k10_margrel1(k9_margrel1(k9_margrel1(c1_4__binari_6)),k9_margrel1(c2_4__binari_6)) = k10_margrel1(c1_4__binari_6,k9_margrel1(c2_4__binari_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__binari_6,dt_c2_4__binari_6])],[commutativity_k10_margrel1,involutiveness_k9_margrel1,dt_k10_margrel1,dt_k9_margrel1,dt_c1_4__binari_6,dt_c2_4__binari_6,cc1_bvfunc_1,fc4_margrel1,fc5_margrel1,rc2_margrel1,t40_margrel1]),
    [interesting(0.65),file(binari_6,e2_4_1__binari_6),[file(binari_6,e2_4_1__binari_6)]]).

fof(e1_4__binari_6,plain,(
    k9_margrel1(k1_bvfunc_1(c1_4__binari_6,c2_4__binari_6)) = k10_margrel1(c1_4__binari_6,k9_margrel1(c2_4__binari_6)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_4__binari_6,dt_c2_4__binari_6])],[e1_4_1__binari_6,e2_4_1__binari_6]),
    [interesting(0.8),file(binari_6,e1_4__binari_6),[file(binari_6,e1_4__binari_6)]]).

fof(i3_4__binari_6,theorem,(
    $true ),
    introduced(tautology,[file(binari_6,i3_4__binari_6)]),
    [interesting(0.8),trivial,file(binari_6,i3_4__binari_6)]).

fof(i2_4__binari_6,plain,(
    k9_margrel1(k1_bvfunc_1(c1_4__binari_6,c2_4__binari_6)) = k10_margrel1(c1_4__binari_6,k9_margrel1(c2_4__binari_6)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__binari_6,dt_c2_4__binari_6])],[e1_4__binari_6,i3_4__binari_6]),
    [interesting(0.8),file(binari_6,i2_4__binari_6),[file(binari_6,i2_4__binari_6)]]).

fof(i2_4_tmp__binari_6,plain,
    ( v2_margrel1(c2_4__binari_6)
   => k9_margrel1(k1_bvfunc_1(c1_4__binari_6,c2_4__binari_6)) = k10_margrel1(c1_4__binari_6,k9_margrel1(c2_4__binari_6)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__binari_6]),discharge_asm(discharge,[dt_c2_4__binari_6])],[dt_c2_4__binari_6,i2_4__binari_6]),
    [interesting(0.8),i1_4__binari_6]).

fof(i1_4__binari_6,plain,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k1_bvfunc_1(c1_4__binari_6,A)) = k10_margrel1(c1_4__binari_6,k9_margrel1(A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__binari_6])],[i2_4_tmp__binari_6,dh_c2_4__binari_6]),
    [interesting(0.8),file(binari_6,i1_4__binari_6),[file(binari_6,i1_4__binari_6)]]).

fof(i1_4_tmp__binari_6,plain,
    ( v2_margrel1(c1_4__binari_6)
   => ! [A] : 
        ( v2_margrel1(A)
       => k9_margrel1(k1_bvfunc_1(c1_4__binari_6,A)) = k10_margrel1(c1_4__binari_6,k9_margrel1(A)) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__binari_6])],[dt_c1_4__binari_6,i1_4__binari_6]),
    [interesting(1),t4_binari_6]).

fof(t4_binari_6,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k9_margrel1(k1_bvfunc_1(A,B)) = k10_margrel1(A,k9_margrel1(B)) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__binari_6,dh_c1_4__binari_6]),
    [interesting(1),file(binari_6,t4_binari_6),[file(binari_6,t4_binari_6)]]).