% Mizar problem: t20_binari_5,binari_5,212,29 
fof(t20_binari_5,conjecture,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k9_margrel1(k5_binari_5(A,B)) = k2_binarith(A,B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_binarith,commutativity_k5_binari_5,involutiveness_k9_margrel1,dt_k2_binarith,dt_k5_binari_5,dt_k9_margrel1,fc3_binari_5,rc2_margrel1,fc4_margrel1,fc2_binarith,cc1_bvfunc_1,d3_binari_5,t40_margrel1]),
    [file(binari_5,t20_binari_5)]).

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

fof(commutativity_k5_binari_5,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k5_binari_5(A,B) = k5_binari_5(B,A) ) ),
    file(binari_5,k5_binari_5),
    []).

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

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

fof(dt_k5_binari_5,axiom,(
    $true ),
    file(binari_5,k5_binari_5),
    []).

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

fof(fc3_binari_5,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => ( v4_ordinal2(k5_binari_5(A,B))
        & v1_xcmplx_0(k5_binari_5(A,B))
        & v2_margrel1(k5_binari_5(A,B))
        & v1_xreal_0(k5_binari_5(A,B)) ) ) ),
    file(binari_5,fc3_binari_5),
    []).

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

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

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

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

fof(d3_binari_5,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k5_binari_5(A,B) = k9_margrel1(k2_binarith(A,B)) ) ) ),
    file(binari_5,d3_binari_5),
    []).

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